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Identifier
Values
=>
Cc0002;cc-rep
[1]=>1 [2]=>1 [1,1]=>2 [3]=>2 [2,1]=>5 [1,1,1]=>9 [4]=>4 [3,1]=>13 [2,2]=>18 [2,1,1]=>34 [1,1,1,1]=>64 [5]=>9 [4,1]=>35 [3,2]=>63 [3,1,1]=>119 [2,2,1]=>171 [2,1,1,1]=>326 [1,1,1,1,1]=>625 [6]=>20 [5,1]=>95 [4,2]=>209 [4,1,1]=>401 [3,3]=>268 [3,2,1]=>744 [3,1,1,1]=>1433 [2,2,2]=>1077 [2,2,1,1]=>2078 [2,1,1,1,1]=>4016 [1,1,1,1,1,1]=>7776 [7]=>48 [6,1]=>262 [5,2]=>683 [5,1,1]=>1316 [4,3]=>1065 [4,2,1]=>2993 [4,1,1,1]=>5799 [3,3,1]=>3868 [3,2,2]=>5637 [3,2,1,1]=>10937 [3,1,1,1,1]=>21256 [2,2,2,1]=>15955 [2,2,1,1,1]=>31022 [2,1,1,1,1,1]=>60387 [1,1,1,1,1,1,1]=>117649 [8]=>115 [7,1]=>727 [6,2]=>2189 [6,1,1]=>4247 [5,3]=>4022 [5,2,1]=>11417 [5,1,1,1]=>22224 [4,4]=>4890 [4,3,1]=>18048 [4,2,2]=>26399 [4,2,1,1]=>51463 [4,1,1,1,1]=>100407 [3,3,2]=>34316 [3,3,1,1]=>66920 [3,2,2,1]=>98005 [3,2,1,1,1]=>191361 [3,1,1,1,1,1]=>373895 [2,2,2,2]=>143568 [2,2,2,1,1]=>280440 [2,2,1,1,1,1]=>548128 [2,1,1,1,1,1,1]=>1071904 [1,1,1,1,1,1,1,1]=>2097152 [9]=>286 [8,1]=>2033 [7,2]=>6951 [7,1,1]=>13532 [6,3]=>14684 [6,2,1]=>41978 [6,1,1,1]=>81987 [5,4]=>20993 [5,3,1]=>78296 [5,2,2]=>114889 [5,2,1,1]=>224670 [5,1,1,1,1]=>439646 [4,4,1]=>95673 [4,3,2]=>183126 [4,3,1,1]=>358318 [4,2,2,1]=>526292 [4,2,1,1,1]=>1030671 [4,1,1,1,1,1]=>2019348 [3,3,3]=>238887 [3,3,2,1]=>686912 [3,3,1,1,1]=>1345583 [3,2,2,2]=>1009360 [3,2,2,1,1]=>1977724 [3,2,1,1,1,1]=>3876719 [3,1,1,1,1,1,1]=>7601777 [2,2,2,2,1]=>2907445 [2,2,2,1,1,1]=>5700489 [2,2,1,1,1,1,1]=>11180483 [2,1,1,1,1,1,1,1]=>21935132 [1,1,1,1,1,1,1,1,1]=>43046721
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Description
The number of coloured rooted trees such that the multiplicities of colours are given by a partition.
In particular, the value on the partition $(n)$ is the number of unlabelled rooted trees on $n$ vertices, oeis:A000081, whereas the value on the partition $(1^n)$ is the number of labelled rooted trees oeis:A000169.
Code
def statistic(mu):
    h = SymmetricFunctions(QQ).h()
    A = CombinatorialSpecies()
    X = species.SingletonSpecies()
    E = species.SetSpecies()
    A.define(X*E(A))
    F = A.cycle_index_series()
    return F.coefficient(mu.size()).scalar(h(mu))

Created
Sep 27, 2020 at 13:05 by Martin Rubey
Updated
Sep 27, 2020 at 13:05 by Martin Rubey