%I #28 Oct 08 2024 13:13:22
%S 1,1,13,13,77,77,78,78,273,273,286,286,429,429,560,560,637,637,715,
%T 715,1001,1001,1001,1001,1287,1287,1365,1365,1716,1716,2002,2002,2079,
%U 2079,4368,4368,4576,4576,4928,4928,5733,5733,6006,6006,6006,6006,6006,6006,6435
%N Degrees of irreducible representations of symmetric group S_14.
%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].
%H Eric M. Schmidt, <a href="/A059796/b059796.txt">Table of n, a(n) for n = 1..135</a> (complete sequence)
%p h:= proc(l) local n; n:= nops(l); add(i, i=l)!/mul(mul(1+l[i]-j+
%p add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n) end:
%p g:= (n, i, l)-> `if`(n=0 or i=1, h([l[], 1$n]), `if`(i<1, 0,
%p seq(g(n-i*j, i-1, [l[], i$j]), j=0..n/i))):
%p sort([g(14$2, [])])[]; # _Alois P. Heinz_, Sep 23 2024
%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[14]] (* _Jean-François Alcover_, Sep 23 2024, after _Alois P. Heinz_ *)
%o (Magma) // See A003875 for MAGMA code.
%o (GAP) List(Irr(CharacterTable("S14")), chi->chi[1]); # _Eric M. Schmidt_, Jul 18 2012
%Y Cf. A003869 - A003877.
%Y Row n=14 of A060240.
%K nonn,fini,full
%O 1,3
%A _N. J. A. Sloane_, Feb 22 2001