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 A361607 #15 Mar 17 2023 09:24:25
%S A361607 1,2,9,88,1457,35226,1158097,49554464,2664907233,175012404562,
%T A361607 13725980234201,1263867766626312,134795551989905809,
%U A361607 16464112185873351338,2280346417134518709537,355060682992984062716176
%N A361607 a(n) = n! * Sum_{k=0..n} binomial(n+(n-1)*k,n*k)/k!.
%F A361607 a(n) = n! * [x^n] exp( x/(1-x)^n ) / (1-x).
%F A361607 a(n) = Sum_{k=0..n} (n*k+n-k)!/(n*k)! * binomial(n,k).
%F A361607 log(a(n)) ~ n*(2*log(n) - log(log(n)) - 1 - log(2) + (log(log(n)) + log(2) + 1/2)/log(n)). - _Vaclav Kotesovec_, Mar 17 2023
%t A361607 Table[Sum[Binomial[n, k]*(n*k + n - k)!/(n*k)!, {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Mar 17 2023 *)
%o A361607 (PARI) a(n) = sum(k=0, n, (n*k+n-k)!/(n*k)!*binomial(n, k));
%Y A361607 Main diagonal of A361600.
%Y A361607 Cf. A293013.
%K A361607 nonn
%O A361607 0,2
%A A361607 _Seiichi Manyama_, Mar 17 2023