OFFSET
1,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..13
EXAMPLE
a(3) = 6 because the sizes of the conjugacy classes in S_3 are 1,2,3 and the product is 6.
MAPLE
b:= proc(n, i) option remember; `if`(n=0 or i=1, [1$2], ((f, g)->
[f[1]+g[1], f[2]*g[2]*i^g[1]])(b(n, i-1), b(n-i, min(n-i, i))))
end:
a:= n-> n!^combinat[numbpart](n)/b(n$2)[2]^2:
seq(a(n), n=1..9); # Alois P. Heinz, Aug 03 2021
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, {1, 1}, Function[{f, g},
{f[[1]] + g[[1]], f[[2]]*g[[2]]*i^g[[1]]}][If[i < 2, {0, 1},
b[n, i-1]], If[i > n, {0, 1}, b[n-i, i]]]];
A007870[n_] := b[n, n][[2]];
a[n_] := (n!)^PartitionsP[n]/A007870[n]^2;
Table[a[n], {n, 1, 9}] (* Jean-François Alcover, Apr 25 2022, after Alois P. Heinz *)
PROG
(Magma) [ &*[ c[2] : c in ClassesData(Sym(n))] : n in [1..10]]; // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
CROSSREFS
KEYWORD
nonn
AUTHOR
Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Sep 30 2001
EXTENSIONS
More terms from Vladeta Jovovic, Oct 04 2001
STATUS
approved