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 A375773 #9 Aug 27 2024 09:12:39
%S A375773 1,0,0,0,0,120,1800,16800,126000,834120,6917400,129399600,3259080000,
%T A375773 72252300120,1370602233000,23218349918400,377834084082000,
%U A375773 6709735404918120,147369456297228600,3899127761438053200,109421543771265852000,3002806840023201408120
%N A375773 Expansion of e.g.f. exp((exp(x) - 1)^5).
%F A375773 G.f.: Sum_{k>=0} (5*k)! * x^(5*k)/(k! * Product_{j=1..5*k} (1 - j * x)).
%F A375773 a(0) = 1; a(n) = 120 * Sum_{k=1..n} binomial(n-1,k-1) * Stirling2(k,5) * a(n-k).
%F A375773 a(n) = Sum_{k=0..floor(n/5)} (5*k)! * Stirling2(n,5*k)/k!.
%o A375773 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((exp(x)-1)^5)))
%o A375773 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=120*sum(j=1, i, binomial(i-1, j-1)*stirling(j, 5, 2)*v[i-j+1])); v;
%o A375773 (PARI) a(n) = sum(k=0, n\5, (5*k)!*stirling(n, 5*k, 2)/k!);
%Y A375773 Cf. A000110, A052859, A353664, A353665.
%Y A375773 Cf. A353404, A373940.
%K A375773 nonn
%O A375773 0,6
%A A375773 _Seiichi Manyama_, Aug 27 2024