A349471 - OEIS

%I #13 Nov 20 2021 08:00:53

%S 1,0,5,71,1625,48699,1815157,80960200,4205895521,249447427145,

%T 16631893722851,1231521399730489,100270564101729529,

%U 8903719880410535595,856322102196977446955,88677383473792696758599,9837660365763014667911553,1163993530309417488368300653

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

%F a(n) ~ exp(n - 1/2) * n^(n - 1/2) / sqrt(2*Pi). - _Vaclav Kotesovec_, Nov 20 2021

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

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

%Y Cf. A226391, A349470.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 19 2021