A358145 a(n) = Sum_{k=0..n} binomial(n*k,k) * binomial(n*(n-k),n-k).

1, 2, 16, 258, 6184, 195660, 7674144, 358788696, 19464910000, 1201543131276, 83134800597280, 6371436086078382, 535715287899894216, 49025879014213908144, 4850781409411286177248, 515964243167132532702480, 58710263012322890445554400

Offset: 0

Author

Seiichi Manyama, Oct 31 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..337

Crossrefs

Main diagonal of A358050.

Programs

PARI

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

PARI

a(n) = sum(k=0, n, (n-1)^(n-k)*binomial(n^2+1, k));

PARI

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

Formula

a(n) = Sum_{k=0..n} (n-1)^(n-k) * binomial(n^2+1,k).

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

a(n) ~ exp(n - 1/2) * n^n / 2. - Vaclav Kotesovec, Nov 01 2022