%I #25 Sep 23 2024 10:10:20
%S 1,1,12,12,65,65,66,66,208,208,220,220,429,429,429,429,429,429,495,
%T 495,572,572,792,792,924,936,936,1287,1287,1365,1365,1430,1430,2574,
%U 2574,2574,2574,2860,2860,3003,3003,3432,3432,3432,3432,3432,3432,3575,3575,3640,3640,4004,4004,4212,4212,4290,4290,5005,5005,5148,5148,5720,5720,6006,6006,6435,6435,6864,6864,7371,7371,7800,7800,8580,8580,8580,9009,9009,9360,9360,10296,10296,11440,11440,11583,11583,12012,12012,12012,12012,12870,12870,15015,15015,16016,17160,17160,20592,20592,21450,21450
%N Degrees of irreducible representations of symmetric group S_13.
%C All 101 terms of this finite sequence are shown.
%D J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites].
%t h[l_] := With[{n = Length[l]}, Total[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 g[n_, i_, l_] := If[n == 0 || i == 1, h[Join[l, Array[1&, n]]], If[i < 1, 0, Flatten@ Table[g[n - i*j, i - 1, Join[l, Array[i &, j]]], {j, 0, n/i}]]];
%t T[n_] := g[n, n, {}];
%t Sort[T[13]] (* _Jean-François Alcover_, Sep 23 2024, after _Alois P. Heinz_ in A060240 *)
%o (Magma) // See A003875 for Magma code.
%o (GAP) A003877 := List(Irr(CharacterTable("S13")), chi->chi[1]);; Sort(A003877); # _Eric M. Schmidt_, Jul 18 2012
%Y Cf. A003869 - A003876, A059796.
%Y Row n=13 of A060240.
%K nonn,fini,full
%O 1,3
%A _N. J. A. Sloane_
%E More terms from _Emeric Deutsch_, May 13 2004