This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A214400 #13 Mar 04 2022 01:58:28 %S A214400 1,4,45,816,20475,658008,25827165,1198774720,64276915527, %T A214400 3911395881900,266401260897200,20082459351180240,1660305826125766950, %U A214400 149389005978091284720,14533945899753270066525,1520398315196482557890304,170190601112537814791748255 %N A214400 a(n) = binomial(n^2 + 3*n, n). %C A214400 Equals the central terms of triangle A214398. %H A214400 Robert Israel, <a href="/A214400/b214400.txt">Table of n, a(n) for n = 0..336</a> %F A214400 a(n) = [x^n] 1/(1 - x)^((n+1)^2). - _Ilya Gutkovskiy_, Oct 04 2017 %F A214400 a(n) ~ n^(n-1/2)*exp(n+5/2)/sqrt(2*Pi). - _Robert Israel_, Mar 04 2022 %p A214400 seq(binomial(n^2+3*n,n),n=0..30); # _Robert Israel_, Mar 04 2022 %o A214400 (PARI) a(n)=binomial(n^2+3*n, n) %Y A214400 Cf. A054688, A178325, A214398. %K A214400 nonn %O A214400 0,2 %A A214400 _Paul D. Hanna_, Jul 15 2012