login
A338787
a(n) = (n!/2) * Sum_{k=1..n-1} A000593(k)*A000593(n-k)/(k*(n-k)).
2
0, 1, 3, 35, 110, 1594, 8064, 125292, 684144, 14215536, 102769920, 2367099360, 18380943360, 463602216960, 4776780072960, 141702567955200, 1382620380825600, 46390044372940800, 550153713457152000, 19877486361997824000, 261552662423506944000, 9914502028911427584000, 146055669195092557824000
OFFSET
1,3
LINKS
FORMULA
a(n) = (n-1)! * Sum_{k=1..n-1} A000593(k)*A000593(n-k)/k.
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 *)
PROG
(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
CROSSREFS
Column 2 of A075525.
Sequence in context: A113854 A231645 A076376 * A353619 A133710 A130061
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 09 2020
STATUS
approved