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 A383132 #7 Apr 19 2025 05:17:12
%S A383132 1,2,33,2701,524993,181752001,97735073905,75179269556672,
%T A383132 78240951854025217,105806762566689176353,180297512864534759056001,
%U A383132 377878889913778527874694227,955217573424445946022789385537,2865620569274978738097814056365899,10064763360358683666070320479027168465
%N A383132 a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n*k,k) * n^k.
%F A383132 a(n) = [x^n] ((1 + n*x)^n + x)^n.
%F A383132 a(n) ~ exp(n - 1/2) * n^(2*n - 1/2) / sqrt(2*Pi). - _Vaclav Kotesovec_, Apr 19 2025
%t A383132 Unprotect[Power]; 0^0 = 1; Table[Sum[Binomial[n, k] Binomial[n k, k] n^k, {k, 0, n}], {n, 0, 14}]
%Y A383132 Cf. A084771, A187021, A331656, A340971, A383120, A383133.
%K A383132 nonn
%O A383132 0,2
%A A383132 _Ilya Gutkovskiy_, Apr 17 2025