%I #34 Sep 23 2024 10:38:46
%S 1,1,4,4,5,5,6
%N Degrees of irreducible representations of symmetric group S_5.
%C All 7 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[5]] (* _Jean-François Alcover_, Sep 22 2024, after _Alois P. Heinz_ in A060240 *)
%o (Magma) // See A003875 for Magma code
%o (GAP) A003869 := List(Irr(CharacterTable("S5")), chi->chi[1]);; Sort(A003869); # _Eric M. Schmidt_, Jul 18 2012
%Y Row n=5 of A060240.
%Y Cf. A003870, A003871, A003872, A003873.
%K nonn,fini,full
%O 1,3
%A _N. J. A. Sloane_