A214400 a(n) = binomial(n^2 + 3*n, n).

1, 4, 45, 816, 20475, 658008, 25827165, 1198774720, 64276915527, 3911395881900, 266401260897200, 20082459351180240, 1660305826125766950, 149389005978091284720, 14533945899753270066525, 1520398315196482557890304, 170190601112537814791748255

Offset: 0

Author

Paul D. Hanna, Jul 15 2012

Keywords

• nonn

Comments

Equals the central terms of triangle A214398.

Links

• Robert Israel, Table of n, a(n) for n = 0..336

Crossrefs

Cf. A054688, A178325, A214398.

Programs

Maple

seq(binomial(n^2+3*n,n),n=0..30); # Robert Israel, Mar 04 2022

PARI

a(n)=binomial(n^2+3*n, n)

Formula

a(n) = [x^n] 1/(1 - x)^((n+1)^2). - Ilya Gutkovskiy, Oct 04 2017

a(n) ~ n^(n-1/2)*exp(n+5/2)/sqrt(2*Pi). - Robert Israel, Mar 04 2022