A348081 a(n) = [x^n] Product_{k=1..2*n} 1/(1 - k^2 * x).

1, 5, 627, 251498, 209609235, 298201326150, 646748606934510, 1986821811445598260, 8209989926930833199235, 43919039258570117113742270, 295300365118450495520630242042, 2437724587984574697761809904387340, 24239364659088896670563082403144467630

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

a(n) ~ c * d^n * n!^2 / n^(3/2), where d = 78.52705817932973261726305432915417900827309581709564977985583533852704254... and c = 0.0815842039686253664272939415761688591712635596695065951780203519... - Vaclav Kotesovec, Oct 16 2021

Mathematica

Table[SeriesCoefficient[Product[1/(1 - k^2*x), {k, 1, 2*n}], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 16 2021 *)

Prog

(PARI) a(n) = polcoef(1/prod(k=1, 2*n, 1-k^2*x+x*O(x^n)), n);

Crossrefs

Cf. A036969, A234324, A298851, A348082.

Sequence in context: A013736 A209589 A060758 * A256070 A203339 A253690

Adjacent sequences: A348078 A348079 A348080 * A348082 A348083 A348084

Keyword

nonn

Author

Seiichi Manyama, Sep 27 2021

Status

approved