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A003876 Degrees of irreducible representations of symmetric group S_12.

%I A003876 #23 Sep 23 2024 10:10:44
%S A003876 1,1,11,11,54,54,55,55,132,132,154,154,165,165,275,275,297,297,320,
%T A003876 320,330,330,462,462,462,462,616,616,891,891,945,945,1155,1155,1320,
%U A003876 1320,1408,1408,1485,1485,1650,1650,1728,1728,1925,1925,1925,1925,2079,2079,2100,2112,2112,2376,2376,2640,2673,2673,2970,2970,3080,3080,3520,3520,3564,3564,3696,3696,4158,4158,4455,4455,5632,5632,5775,5775,7700
%N A003876 Degrees of irreducible representations of symmetric group S_12.
%C A003876 All 77 terms of this finite sequence are shown.
%D A003876 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 A003876 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 A003876 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 A003876 T[n_] := g[n, n, {}];
%t A003876 Sort[T[12]] (* _Jean-François Alcover_, Sep 23 2024, after _Alois P. Heinz_ in A060240 *)
%o A003876 (Magma) // See A003875 for Magma code.
%o A003876 (GAP) A003876 := List(Irr(CharacterTable("S12")), chi->chi[1]);; Sort(A003876); # _Eric M. Schmidt_, Jul 18 2012
%Y A003876 Row n=12 of A060240.
%K A003876 nonn,fini,full
%O A003876 1,3
%A A003876 _N. J. A. Sloane_