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A059796 Degrees of irreducible representations of symmetric group S_14.

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