OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..444
EXAMPLE
a(4) = 44 because in the conjugacy classes of S(4): (4), (3)(1), (2)(2), (2)(1)(1), (1)(1)(1)(1) there are (respectively) 6 permutations times 1 arrangement, 8 permutations times 2 arrangements, 3 permutations times 1 arrangement, 6 permutations times 3 arrangements, and 1 permutation times 1 arrangement. So 6*1+8*2+3*1+6*3+1*1 = 44.
MAPLE
b:= proc(n, i, p) option remember; `if`(n=0 or i=1,
(p+n)!/n!, add(b(n-i*j, i-1, p+j)*(i-1)!^j*combinat
[multinomial](n, n-i*j, i$j)/j!^2, j=0..n/i))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..25); # Alois P. Heinz, Apr 27 2017
MATHEMATICA
Needs["Combinatorica`"]; f[{x_, y_}]:= x^y y!; Table[Total[Table[n!, {PartitionsP[n]}]/Apply[Times, Map[f, Map[Tally, Partitions[n]], {2}], 2] * Apply[Multinomial, Map[Last, Map[Tally, Partitions[n]], {2}], 2]], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Sep 30 2011
STATUS
approved