A358145 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

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

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

PROG

(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));