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A064430 Product of the sizes of the conjugacy classes of the symmetric group S_n. 1
1, 1, 6, 864, 43200000, 272097792000000000, 3416681839784939886182400000000000, 1847600699255039694224318542233446367734016245760000000000000000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 30 18:49 EST 2023. Contains 359947 sequences. (Running on oeis4.)