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 A331512 #22 May 05 2021 01:52:36
%S A331512 1,8,90,1328,24150,520272,12926004,363233600,11376760230,392615960600,
%T A331512 14791582824876,603743206301424,26528443526357500,1248071683342913184,
%U A331512 62576263671773466600,3330116426356595493120,187430800395881065513734
%N A331512 a(n) = Sum_{k=0..n} n^(n-k) * (n+k+1) * binomial(n,k) * binomial(n+k,k).
%H A331512 Seiichi Manyama, <a href="/A331512/b331512.txt">Table of n, a(n) for n = 0..380</a>
%F A331512 a(n) = [x^n] (1 - n*x)/(1 - 2*(n+2)*x + (n*x)^2)^(3/2).
%F A331512 a(n) = Sum_{k=0..n} (n+1)^k * (k+1) * binomial(n+1,k+1)^2.
%t A331512 a[n_] := Sum[If[n == n-k == 0, 1, n^(n-k)] * (n+k+1) * Binomial[n, k] * Binomial[n + k, k], {k, 0, n}]; Array[a, 17, 0] (* _Amiram Eldar_, May 05 2021 *)
%o A331512 (PARI) {a(n) = sum(k=0, n, n^(n-k)*(n+k+1)*binomial(n, k)*binomial(n+k, k))}
%o A331512 (PARI) {a(n) = polcoef((1-n*x)/(1-2*(n+2)*x+(n*x)^2)^(3/2), n)}
%o A331512 (PARI) {a(n) = sum(k=0, n, (n+1)^k*(k+1)*binomial(n+1, k+1)^2)}
%Y A331512 Cf. A001850, A108666, A331511, A331513.
%K A331512 nonn
%O A331512 0,2
%A A331512 _Seiichi Manyama_, Jan 19 2020