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

%I A129627 #24 May 18 2017 03:48:23
%S A129627 1,2,18,180,3060,101160,3807720,174986280,10699554600,927701102160,
%T A129627 95030461809360,10905467528783520,1431935974242053280,
%U A129627 222906109589537774400,42471495822490670295360,9447237366839585591438160,2329156499421828313498781520
%N A129627 Sum of the 4th powers of the degrees of irreducible representations of S_n, the symmetric group on n letters.
%C A129627 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
%H A129627 Alois P. Heinz, <a href="/A129627/b129627.txt">Table of n, a(n) for n = 1..60</a>
%H A129627 Thotsaporn Thanatipanonda, <a href="/A129627/a129627.txt">Maple code for A129627</a>
%t A129627 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}]];
%t A129627 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]]]]];
%t A129627 a[n_] := If[n == 0, 1, g[n, n, 4, {}]];
%t A129627 Table[a[n], {n, 1, 20}] (* _Jean-François Alcover_, May 18 2017, after _Alois P. Heinz_ *)
%o A129627 (GAP) List([1..20],n->Sum(List(Irr(CharacterTable("Symmetric",n)), x->x[1]^4)));
%Y A129627 Cf. A000142, A000085.
%Y A129627 Column k=4 of A208447. - _Alois P. Heinz_, Feb 28 2012
%K A129627 nonn
%O A129627 1,2
%A A129627 _Dmitrii Pasechnik_, May 30 2007