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-----------------------------------------------------------------------------
Statistic identifier: St000707
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The product of the factorials of the parts.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(la):
return prod(factorial(p) for p in la)
-----------------------------------------------------------------------------
Statistic values:
[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
-----------------------------------------------------------------------------
Created: Mar 07, 2017 at 09:36 by Martin Rubey
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Last Updated: Mar 07, 2017 at 09:36 by Martin Rubey