%I #13 Mar 04 2022 01:58:28
%S 1,4,45,816,20475,658008,25827165,1198774720,64276915527,
%T 3911395881900,266401260897200,20082459351180240,1660305826125766950,
%U 149389005978091284720,14533945899753270066525,1520398315196482557890304,170190601112537814791748255
%N a(n) = binomial(n^2 + 3*n, n).
%C Equals the central terms of triangle A214398.
%H Robert Israel, <a href="/A214400/b214400.txt">Table of n, a(n) for n = 0..336</a>
%F a(n) = [x^n] 1/(1 - x)^((n+1)^2). - _Ilya Gutkovskiy_, Oct 04 2017
%F a(n) ~ n^(n-1/2)*exp(n+5/2)/sqrt(2*Pi). - _Robert Israel_, Mar 04 2022
%p seq(binomial(n^2+3*n,n),n=0..30); # _Robert Israel_, Mar 04 2022
%o (PARI) a(n)=binomial(n^2+3*n, n)
%Y Cf. A054688, A178325, A214398.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 15 2012