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 A378410 #5 Nov 27 2024 07:14:56
%S A378410 1,1,1,7,85,1581,40006,1288729,50578445,2344950745,125538581926,
%T A378410 7626452229331,518557071012696,39027861427630167,3221686807607369921,
%U A378410 289464281567009809303,28124498248184961490621,2938498159807193630239281,328556126358414341918608978
%N A378410 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,k-1) * binomial(n*k,k) / ((n-1)*k+1).
%F A378410 a(n) ~ exp(n - 1/2 - 1/exp(1)) * n^(n - 5/2) / sqrt(2*Pi).
%t A378410 Table[Sum[(-1)^(n-k) * Binomial[n-1, k-1] * Binomial[n*k, k]/((n-1)*k + 1), {k, 0, n}], {n, 0, 20}]
%Y A378410 Cf. A349364, A378326, A378327, A378409.
%K A378410 nonn
%O A378410 0,4
%A A378410 _Vaclav Kotesovec_, Nov 25 2024