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 A383133 #6 Apr 19 2025 05:22:14
%S A383133 1,0,17,1889,412225,151448249,84430503361,66535567456546,
%T A383133 70456680210155009,96530372235620300465,166169585125820280654001,
%U A383133 351113456811120647774884511,893491183170443755035588745153,2695374684029443253628238600963667,9511442599320236554084097413617603681
%N A383133 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(n*k,k) * n^k.
%F A383133 a(n) = [x^n] ((1 + n*x)^n - x)^n.
%F A383133 a(n) ~ exp(n - 1/2) * n^(2*n - 1/2) / sqrt(2*Pi). - _Vaclav Kotesovec_, Apr 19 2025
%t A383133 Unprotect[Power]; 0^0 = 1; Table[Sum[(-1)^(n - k) Binomial[n, k] Binomial[n k, k] n^k, {k, 0, n}], {n, 0, 14}]
%Y A383133 Cf. A307885, A331657, A340972, A383121, A383132.
%K A383133 nonn
%O A383133 0,3
%A A383133 _Ilya Gutkovskiy_, Apr 17 2025