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

0,2

Comments

Equals the central terms of triangle A214398.

Links

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

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

Maple

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

Prog

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

Crossrefs

Cf. A054688, A178325, A214398.

Sequence in context: A377550 A126747 A107668 * A360344 A197989 A377830

Adjacent sequences: A214397 A214398 A214399 * A214401 A214402 A214403

Keyword

nonn

Author

Paul D. Hanna, Jul 15 2012

Status

approved