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A338787 a(n) = (n!/2) * Sum_{k=1..n-1} A000593(k)*A000593(n-k)/(k*(n-k)).

%I A338787 #20 Nov 10 2020 02:19:17
%S A338787 0,1,3,35,110,1594,8064,125292,684144,14215536,102769920,2367099360,
%T A338787 18380943360,463602216960,4776780072960,141702567955200,
%U A338787 1382620380825600,46390044372940800,550153713457152000,19877486361997824000,261552662423506944000,9914502028911427584000,146055669195092557824000
%N A338787 a(n) = (n!/2) * Sum_{k=1..n-1} A000593(k)*A000593(n-k)/(k*(n-k)).
%H A338787 Seiichi Manyama, <a href="/A338787/b338787.txt">Table of n, a(n) for n = 1..449</a>
%F A338787 a(n) = (n-1)! * Sum_{k=1..n-1} A000593(k)*A000593(n-k)/k.
%t A338787 nmax = 30; A000593 = Table[Sum[Mod[d, 2] d, {d, Divisors[n]}], {n, 1, nmax}]; Table[n!/2 * Sum[A000593[[k]] * A000593[[n-k]] / k / (n-k), {k, 1, n-1}], {n, 1, nmax}] (* _Vaclav Kotesovec_, Nov 09 2020 *)
%o A338787 (PARI) {a(n) = my(t='t); n!*polcoef(polcoef(prod(k=1, n, (1+x^k+x*O(x^n))^t), n), 2)}
%o A338787 (PARI) sod(n) = sigma(n>>valuation(n, 2)); \\ A000593
%o A338787 a(n) = (n!/2) * sum(k=1, n-1, sod(k)*sod(n-k)/(k*(n-k))); \\ _Michel Marcus_, Nov 09 2020
%Y A338787 Column 2 of A075525.
%Y A338787 Cf. A000593, A059356.
%K A338787 nonn
%O A338787 1,3
%A A338787 _Seiichi Manyama_, Nov 09 2020