- FindStat

Identifier

St000707: Integer partitions ⟶ ℤ

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

                        [2]=>2
[1,1]=>1
[3]=>6
[2,1]=>2
[1,1,1]=>1
[4]=>24
[3,1]=>6
[2,2]=>4
[2,1,1]=>2
[1,1,1,1]=>1
[5]=>120
[4,1]=>24
[3,2]=>12
[3,1,1]=>6
[2,2,1]=>4
[2,1,1,1]=>2
[1,1,1,1,1]=>1
[6]=>720
[5,1]=>120
[4,2]=>48
[4,1,1]=>24
[3,3]=>36
[3,2,1]=>12
[3,1,1,1]=>6
[2,2,2]=>8
[2,2,1,1]=>4
[2,1,1,1,1]=>2
[1,1,1,1,1,1]=>1
[7]=>5040
[6,1]=>720
[5,2]=>240
[5,1,1]=>120
[4,3]=>144
[4,2,1]=>48
[4,1,1,1]=>24
[3,3,1]=>36
[3,2,2]=>24
[3,2,1,1]=>12
[3,1,1,1,1]=>6
[2,2,2,1]=>8
[2,2,1,1,1]=>4
[2,1,1,1,1,1]=>2
[1,1,1,1,1,1,1]=>1
[8]=>40320
[7,1]=>5040
[6,2]=>1440
[6,1,1]=>720
[5,3]=>720
[5,2,1]=>240
[5,1,1,1]=>120
[4,4]=>576
[4,3,1]=>144
[4,2,2]=>96
[4,2,1,1]=>48
[4,1,1,1,1]=>24
[3,3,2]=>72
[3,3,1,1]=>36
[3,2,2,1]=>24
[3,2,1,1,1]=>12
[3,1,1,1,1,1]=>6
[2,2,2,2]=>16
[2,2,2,1,1]=>8
[2,2,1,1,1,1]=>4
[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1]=>1
[9]=>362880
[8,1]=>40320
[7,2]=>10080
[7,1,1]=>5040
[6,3]=>4320
[6,2,1]=>1440
[6,1,1,1]=>720
[5,4]=>2880
[5,3,1]=>720
[5,2,2]=>480
[5,2,1,1]=>240
[5,1,1,1,1]=>120
[4,4,1]=>576
[4,3,2]=>288
[4,3,1,1]=>144
[4,2,2,1]=>96
[4,2,1,1,1]=>48
[4,1,1,1,1,1]=>24
[3,3,3]=>216
[3,3,2,1]=>72
[3,3,1,1,1]=>36
[3,2,2,2]=>48
[3,2,2,1,1]=>24
[3,2,1,1,1,1]=>12
[3,1,1,1,1,1,1]=>6
[2,2,2,2,1]=>16
[2,2,2,1,1,1]=>8
[2,2,1,1,1,1,1]=>4
[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1]=>1
[10]=>3628800
[9,1]=>362880
[8,2]=>80640
[8,1,1]=>40320
[7,3]=>30240
[7,2,1]=>10080
[7,1,1,1]=>5040
[6,4]=>17280
[6,3,1]=>4320
[6,2,2]=>2880
[6,2,1,1]=>1440
[6,1,1,1,1]=>720
[5,5]=>14400
[5,4,1]=>2880
[5,3,2]=>1440
[5,3,1,1]=>720
[5,2,2,1]=>480
[5,2,1,1,1]=>240
[5,1,1,1,1,1]=>120
[4,4,2]=>1152
[4,4,1,1]=>576
[4,3,3]=>864
[4,3,2,1]=>288
[4,3,1,1,1]=>144
[4,2,2,2]=>192
[4,2,2,1,1]=>96
[4,2,1,1,1,1]=>48
[4,1,1,1,1,1,1]=>24
[3,3,3,1]=>216
[3,3,2,2]=>144
[3,3,2,1,1]=>72
[3,3,1,1,1,1]=>36
[3,2,2,2,1]=>48
[3,2,2,1,1,1]=>24
[3,2,1,1,1,1,1]=>12
[3,1,1,1,1,1,1,1]=>6
[2,2,2,2,2]=>32
[2,2,2,2,1,1]=>16
[2,2,2,1,1,1,1]=>8
[2,2,1,1,1,1,1,1]=>4
[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1]=>1
[11]=>39916800
[10,1]=>3628800
[9,2]=>725760
[9,1,1]=>362880
[8,3]=>241920
[8,2,1]=>80640
[8,1,1,1]=>40320
[7,4]=>120960
[7,3,1]=>30240
[7,2,2]=>20160
[7,2,1,1]=>10080
[7,1,1,1,1]=>5040
[6,5]=>86400
[6,4,1]=>17280
[6,3,2]=>8640
[6,3,1,1]=>4320
[6,2,2,1]=>2880
[6,2,1,1,1]=>1440
[6,1,1,1,1,1]=>720
[5,5,1]=>14400
[5,4,2]=>5760
[5,4,1,1]=>2880
[5,3,3]=>4320
[5,3,2,1]=>1440
[5,3,1,1,1]=>720
[5,2,2,2]=>960
[5,2,2,1,1]=>480
[5,2,1,1,1,1]=>240
[5,1,1,1,1,1,1]=>120
[4,4,3]=>3456
[4,4,2,1]=>1152
[4,4,1,1,1]=>576
[4,3,3,1]=>864
[4,3,2,2]=>576
[4,3,2,1,1]=>288
[4,3,1,1,1,1]=>144
[4,2,2,2,1]=>192
[4,2,2,1,1,1]=>96
[4,2,1,1,1,1,1]=>48
[4,1,1,1,1,1,1,1]=>24
[3,3,3,2]=>432
[3,3,3,1,1]=>216
[3,3,2,2,1]=>144
[3,3,2,1,1,1]=>72
[3,3,1,1,1,1,1]=>36
[3,2,2,2,2]=>96
[3,2,2,2,1,1]=>48
[3,2,2,1,1,1,1]=>24
[3,2,1,1,1,1,1,1]=>12
[3,1,1,1,1,1,1,1,1]=>6
[2,2,2,2,2,1]=>32
[2,2,2,2,1,1,1]=>16
[2,2,2,1,1,1,1,1]=>8
[2,2,1,1,1,1,1,1,1]=>4
[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1,1]=>1
[12]=>479001600
[11,1]=>39916800
[10,2]=>7257600
[10,1,1]=>3628800
[9,3]=>2177280
[9,2,1]=>725760
[9,1,1,1]=>362880
[8,4]=>967680
[8,3,1]=>241920
[8,2,2]=>161280
[8,2,1,1]=>80640
[8,1,1,1,1]=>40320
[7,5]=>604800
[7,4,1]=>120960
[7,3,2]=>60480
[7,3,1,1]=>30240
[7,2,2,1]=>20160
[7,2,1,1,1]=>10080
[7,1,1,1,1,1]=>5040
[6,6]=>518400
[6,5,1]=>86400
[6,4,2]=>34560
[6,4,1,1]=>17280
[6,3,3]=>25920
[6,3,2,1]=>8640
[6,3,1,1,1]=>4320
[6,2,2,2]=>5760
[6,2,2,1,1]=>2880
[6,2,1,1,1,1]=>1440
[6,1,1,1,1,1,1]=>720
[5,5,2]=>28800
[5,5,1,1]=>14400
[5,4,3]=>17280
[5,4,2,1]=>5760
[5,4,1,1,1]=>2880
[5,3,3,1]=>4320
[5,3,2,2]=>2880
[5,3,2,1,1]=>1440
[5,3,1,1,1,1]=>720
[5,2,2,2,1]=>960
[5,2,2,1,1,1]=>480
[5,2,1,1,1,1,1]=>240
[5,1,1,1,1,1,1,1]=>120
[4,4,4]=>13824
[4,4,3,1]=>3456
[4,4,2,2]=>2304
[4,4,2,1,1]=>1152
[4,4,1,1,1,1]=>576
[4,3,3,2]=>1728
[4,3,3,1,1]=>864
[4,3,2,2,1]=>576
[4,3,2,1,1,1]=>288
[4,3,1,1,1,1,1]=>144
[4,2,2,2,2]=>384
[4,2,2,2,1,1]=>192
[4,2,2,1,1,1,1]=>96
[4,2,1,1,1,1,1,1]=>48
[4,1,1,1,1,1,1,1,1]=>24
[3,3,3,3]=>1296
[3,3,3,2,1]=>432
[3,3,3,1,1,1]=>216
[3,3,2,2,2]=>288
[3,3,2,2,1,1]=>144
[3,3,2,1,1,1,1]=>72
[3,3,1,1,1,1,1,1]=>36
[3,2,2,2,2,1]=>96
[3,2,2,2,1,1,1]=>48
[3,2,2,1,1,1,1,1]=>24
[3,2,1,1,1,1,1,1,1]=>12
[3,1,1,1,1,1,1,1,1,1]=>6
[2,2,2,2,2,2]=>64
[2,2,2,2,2,1,1]=>32
[2,2,2,2,1,1,1,1]=>16
[2,2,2,1,1,1,1,1,1]=>8
[2,2,1,1,1,1,1,1,1,1]=>4
[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1,1,1]=>1
                    

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$F_{2} = q + q^{2}$

$F_{3} = q + q^{2} + q^{6}$

$F_{4} = q + q^{2} + q^{4} + q^{6} + q^{24}$

$F_{5} = q + q^{2} + q^{4} + q^{6} + q^{12} + q^{24} + q^{120}$

$F_{6} = q + q^{2} + q^{4} + q^{6} + q^{8} + q^{12} + q^{24} + q^{36} + q^{48} + q^{120} + q^{720}$

$F_{7} = q + q^{2} + q^{4} + q^{6} + q^{8} + q^{12} + 2\ q^{24} + q^{36} + q^{48} + q^{120} + q^{144} + q^{240} + q^{720} + q^{5040}$

$F_{8} = q + q^{2} + q^{4} + q^{6} + q^{8} + q^{12} + q^{16} + 2\ q^{24} + q^{36} + q^{48} + q^{72} + q^{96} + q^{120} + q^{144} + q^{240} + q^{576} + 2\ q^{720} + q^{1440} + q^{5040} + q^{40320}$

$F_{9} = q + q^{2} + q^{4} + q^{6} + q^{8} + q^{12} + q^{16} + 2\ q^{24} + q^{36} + 2\ q^{48} + q^{72} + q^{96} + q^{120} + q^{144} + q^{216} + q^{240} + q^{288} + q^{480} + q^{576} + 2\ q^{720} + q^{1440} + q^{2880} + q^{4320} + q^{5040} + q^{10080} + q^{40320} + q^{362880}$

$F_{10} = q + q^{2} + q^{4} + q^{6} + q^{8} + q^{12} + q^{16} + 2\ q^{24} + q^{32} + q^{36} + 2\ q^{48} + q^{72} + q^{96} + q^{120} + 2\ q^{144} + q^{192} + q^{216} + q^{240} + q^{288} + q^{480} + q^{576} + 2\ q^{720} + q^{864} + q^{1152} + 2\ q^{1440} + 2\ q^{2880} + q^{4320} + q^{5040} + q^{10080} + q^{14400} + q^{17280} + q^{30240} + q^{40320} + q^{80640} + q^{362880} + q^{3628800}$

$F_{11} = q + q^{2} + q^{4} + q^{6} + q^{8} + q^{12} + q^{16} + 2\ q^{24} + q^{32} + q^{36} + 2\ q^{48} + q^{72} + 2\ q^{96} + q^{120} + 2\ q^{144} + q^{192} + q^{216} + q^{240} + q^{288} + q^{432} + q^{480} + 2\ q^{576} + 2\ q^{720} + q^{864} + q^{960} + q^{1152} + 2\ q^{1440} + 2\ q^{2880} + q^{3456} + 2\ q^{4320} + q^{5040} + q^{5760} + q^{8640} + q^{10080} + q^{14400} + q^{17280} + q^{20160} + q^{30240} + q^{40320} + q^{80640} + q^{86400} + q^{120960} + q^{241920} + q^{362880} + q^{725760} + q^{3628800} + q^{39916800}$

$F_{12} = q + q^{2} + q^{4} + q^{6} + q^{8} + q^{12} + q^{16} + 2\ q^{24} + q^{32} + q^{36} + 2\ q^{48} + q^{64} + q^{72} + 2\ q^{96} + q^{120} + 2\ q^{144} + q^{192} + q^{216} + q^{240} + 2\ q^{288} + q^{384} + q^{432} + q^{480} + 2\ q^{576} + 2\ q^{720} + q^{864} + q^{960} + q^{1152} + q^{1296} + 2\ q^{1440} + q^{1728} + q^{2304} + 3\ q^{2880} + q^{3456} + 2\ q^{4320} + q^{5040} + 2\ q^{5760} + q^{8640} + q^{10080} + q^{13824} + q^{14400} + 2\ q^{17280} + q^{20160} + q^{25920} + q^{28800} + q^{30240} + q^{34560} + q^{40320} + q^{60480} + q^{80640} + q^{86400} + q^{120960} + q^{161280} + q^{241920} + q^{362880} + q^{518400} + q^{604800} + q^{725760} + q^{967680} + q^{2177280} + q^{3628800} + q^{7257600} + q^{39916800} + q^{479001600}$

Description

The product of the factorials of the parts.

Code

def statistic(la):
    return prod(factorial(p) for p in la)

Created

Mar 07, 2017 at 09:36 by Martin Rubey

Updated

Mar 07, 2017 at 09:36 by Martin Rubey