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A257675 a(n) = A257673(2n,n).

%I A257675 #19 Aug 23 2021 05:54:43
%S A257675 1,3,21,174,1509,13473,122580,1129999,10518477,98644395,930607321,
%T A257675 8821717743,83960385396,801783097911,7678690148647,73721697254874,
%U A257675 709323064431597,6837868454315828,66028546945097793,638555320797561440,6183787002091288969,59957399899953193063
%N A257675 a(n) = A257673(2n,n).
%H A257675 Alois P. Heinz, <a href="/A257675/b257675.txt">Table of n, a(n) for n = 0..500</a>
%F A257675 a(n) = A257673(2n,n).
%F A257675 a(n) ~ c * d^n / sqrt(n), where d = 9.93288639318036180192949205242384178223421389697248991016311001938239..., c = 0.31807008223273549425589833682845775837952038959... . - _Vaclav Kotesovec_, May 19 2015
%F A257675 a(n) = [x^(2*n)] (-1 + Product_{k>=1} 1 / (1 - x^k)^k)^n. - _Ilya Gutkovskiy_, Feb 13 2021
%p A257675 g:= proc(n) option remember; `if`(n=0, 1, add(
%p A257675       g(n-j)*numtheory[sigma][2](j), j=1..n)/n)
%p A257675     end:
%p A257675 b:= proc(n, k) option remember; `if`(k<2, g(n+1), (q->
%p A257675       add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
%p A257675     end:
%p A257675 a:= n-> b(n$2):
%p A257675 seq(a(n), n=0..22);
%t A257675 g[n_] := g[n] = If[n == 0, 1, Sum[g[n - j]*
%t A257675      DivisorSigma[2, j], {j, 1, n}]/n];
%t A257675 b[n_, k_] := b[n, k] = If[k < 2, g[n+1], With[{q = Quotient[k, 2]},
%t A257675      Sum[b[j, q] b[n - j, k - q], {j, 0, n}]]];
%t A257675 a[n_] := b[n, n];
%t A257675 Table[a[n], {n, 0, 22}] (* _Jean-François Alcover_, Aug 23 2021, after _Alois P. Heinz_ *)
%Y A257675 Cf. A000219, A257673.
%K A257675 nonn
%O A257675 0,2
%A A257675 _Alois P. Heinz_, May 03 2015