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A089248 a(n) is the sum of the odd degrees of the irreducible representations of the symmetric group S_n.

%I A089248 #14 Sep 23 2024 10:31:47
%S A089248 1,2,2,8,12,40,144,128,644,3504,7000,48224,130992,861792,3257600,
%T A089248 32768,425988,5833312,27621672,415526656,1987852432,17674429440,
%U A089248 157807273408,265515959680,2848581615344,30980959604096,114059874705248,1365388896050048,6215927122198944
%N A089248 a(n) is the sum of the odd degrees of the irreducible representations of the symmetric group S_n.
%C A089248 a(n) is divisible by 4 for n >= 4. - _Eric M. Schmidt_, Apr 28 2013
%D A089248 John McKay, Irreducible representations of odd degree, Journal of Algebra 20, 1972 pages 416-418.
%H A089248 Eric M. Schmidt, <a href="/A089248/b089248.txt">Table of n, a(n) for n = 1..200</a>
%H A089248 Eric M. Schmidt, <a href="/A089248/a089248.sage.txt">Sage code to compute this sequence</a>
%F A089248 a(2^n) = 2^(2^n - 1). - _Eric M. Schmidt_, Apr 28 2013
%t A089248 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 A089248 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 A089248 a[n_] := a[n] = If[n == 1, 1, Select[g[n, n, {}], OddQ] // Total];
%t A089248 Table[Print[n, " ", a[n]];
%t A089248 a[n], {n, 1, 50}] (* _Jean-François Alcover_, Sep 23 2024, after _Alois P. Heinz_ in A060240 *)
%o A089248 (Sage)
%o A089248 # Simple but inefficient; see links for faster code
%o A089248 def A089248(n) :
%o A089248     res = 0
%o A089248     for P in Partitions(n) :
%o A089248         deg = P.dimension()
%o A089248         if is_odd(deg) : res += deg
%o A089248     return res
%o A089248 # _Eric M. Schmidt_, Apr 28 2013
%Y A089248 Cf. A000085, A059867.
%K A089248 nonn
%O A089248 1,2
%A A089248 Yuval Dekel (dekelyuval(AT)hotmail.com), Dec 11 2003
%E A089248 More terms from _Eric M. Schmidt_, Apr 28 2013