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 A378409 #9 Nov 27 2024 07:13:52
%S A378409 1,0,1,5,73,1409,36601,1198798,47594289,2225255777,119896198381,
%T A378409 7320401163591,499766786359501,37739036987427515,3123975386959740223,
%U A378409 281348109008473891049,27391364013973766381281,2866934827195653717595713,321048532728871544387444869,38303867032042004479765603315
%N A378409 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(n*k,k) / ((n-1)*k+1).
%F A378409 a(n) ~ exp(n - 1/2 - 1/exp(1)) * n^(n - 5/2) / sqrt(2*Pi).
%t A378409 Table[Sum[(-1)^(n-k) * Binomial[n, k] * Binomial[n*k, k]/((n-1)*k + 1), {k, 0, n}], {n, 0, 20}]
%Y A378409 Cf. A346668, A378326, A378327, A378410.
%K A378409 nonn
%O A378409 0,4
%A A378409 _Vaclav Kotesovec_, Nov 25 2024