A064430 Product of the sizes of the conjugacy classes of the symmetric group S_n.

1, 1, 6, 864, 43200000, 272097792000000000, 3416681839784939886182400000000000, 1847600699255039694224318542233446367734016245760000000000000000

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..13

Formula

a(n) = (n!)^A000041(n) / A007870(n)^2.

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

Cf. A007870, A000041, A063073, A000142.

Sequence in context: A281690 A201141 A078927 * A332186 A279304 A180992

Adjacent sequences: A064427 A064428 A064429 * A064431 A064432 A064433

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