%I #22 Sep 22 2024 15:20:05
%S 1,1,6,6,14,14,14,14,15,15,20,21,21,35,35
%N Degrees of irreducible representations of symmetric group S_7.
%C All 15 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[7]] (* _Jean-François Alcover_, Sep 22 2024, after _Alois P. Heinz_ in A060240 *)
%o (GAP) A003871 := List(Irr(CharacterTable("S7")), chi->chi[1]);; Sort(A003871); # _Eric M. Schmidt_, Jul 18 2012
%Y Row n=7 of A060240.
%K nonn,fini,full
%O 1,3
%A _N. J. A. Sloane_