A335096 a(n) = ((2*n+1)!!)^n * (Sum_{k=1..n} 1/(2*k+1)^n).

0, 1, 34, 55511, 11575291716, 548347875819272649, 8811385079228718926321932614, 66303398534111438173105653188803948359375, 308529654991526005900670429792887300937160115962403125000

Offset: 0

Author

Seiichi Manyama, Sep 12 2020

Keywords

• nonn

Crossrefs

Main diagonal of A335095.

Cf. A291676.

Programs

Mathematica

Table[((2*n + 1)!!)^n * Sum[1/(2*k + 1)^n, {k, 1, n}], {n, 0, 10}] (* Vaclav Kotesovec, Sep 25 2020 *)

PARI

{a(n) = prod(k=1, n, 2*k+1)^n*sum(k=1, n, 1/(2*k+1)^n)}

Formula

a(n) ~ 2^(n*(n + 3/2)) * n^(n*(n+1)) / (3^n * exp(n^2 - 11/24)). - Vaclav Kotesovec, Sep 25 2020