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

0, 1, 3, 35, 110, 1594, 8064, 125292, 684144, 14215536, 102769920, 2367099360, 18380943360, 463602216960, 4776780072960, 141702567955200, 1382620380825600, 46390044372940800, 550153713457152000, 19877486361997824000, 261552662423506944000, 9914502028911427584000, 146055669195092557824000

Offset: 1

Author

Seiichi Manyama, Nov 09 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..449

Crossrefs

Column 2 of A075525.

Cf. A000593, A059356.

Programs

Mathematica

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 *)

PARI

{a(n) = my(t='t); n!*polcoef(polcoef(prod(k=1, n, (1+x^k+x*O(x^n))^t), n), 2)}

PARI

sod(n) = sigma(n>>valuation(n, 2)); \\ A000593
a(n) = (n!/2) * sum(k=1, n-1, sod(k)*sod(n-k)/(k*(n-k))); \\ Michel Marcus, Nov 09 2020

Formula

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