A349471 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(k*n,k).

1, 0, 5, 71, 1625, 48699, 1815157, 80960200, 4205895521, 249447427145, 16631893722851, 1231521399730489, 100270564101729529, 8903719880410535595, 856322102196977446955, 88677383473792696758599, 9837660365763014667911553, 1163993530309417488368300653

Offset: 0

Author

Seiichi Manyama, Nov 19 2021

Keywords

• nonn

Crossrefs

Cf. A226391, A349470.

Programs

Mathematica

a[n_] := Sum[(-1)^(n - k) * Binomial[k*n, k], {k, 0, n}]; Array[a, 20, 0] (* Amiram Eldar, Nov 19 2021 *)

PARI

a(n) = sum(k=0, n, (-1)^(n-k)*binomial(k*n, k));

Formula

a(n) ~ exp(n - 1/2) * n^(n - 1/2) / sqrt(2*Pi). - Vaclav Kotesovec, Nov 20 2021