A129627 Sum of the 4th powers of the degrees of irreducible representations of S_n, the symmetric group on n letters.

1, 2, 18, 180, 3060, 101160, 3807720, 174986280, 10699554600, 927701102160, 95030461809360, 10905467528783520, 1431935974242053280, 222906109589537774400, 42471495822490670295360, 9447237366839585591438160, 2329156499421828313498781520

Offset: 1

Author

Dmitrii Pasechnik, May 30 2007

Keywords

• nonn

Comments

a(n) is also the sum of the fourth powers of the numbers of standard Young tableaux over all partitions of n. - Thotsaporn Thanatipanonda, Feb 25 2012

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..60
• Thotsaporn Thanatipanonda, Maple code for A129627

Crossrefs

Cf. A000142, A000085.

Column k=4 of A208447. - Alois P. Heinz, Feb 28 2012

Programs

GAP

List([1..20],n->Sum(List(Irr(CharacterTable("Symmetric",n)), x->x[1]^4)));

Mathematica

h[l_] := With[{n=Length[l]}, Sum[i, {i, l}]!/Product[Product[1 + l[[i]] - j + Sum[If[l[[k]] >= j, 1, 0], {k, i+1, n}], {j, 1, l[[i]]}], {i, 1, n}]];
g[n_, i_, k_, l_] := g[n, i, l, k] = If[n == 0, h[l]^k, If[i < 1, 0, g[n, i - 1, k, l] + If[i > n, 0, g[n - i, i, k, Append[l, i]]]]];
a[n_] := If[n == 0, 1, g[n, n, 4, {}]];
Table[a[n], {n, 1, 20}] (* Jean-François Alcover, May 18 2017, after Alois P. Heinz *)