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 A380917 #7 Feb 08 2025 10:29:55
%S A380917 1,4,31,453,9957,293103,10850625,484699491,25381819737,1525299702363,
%T A380917 103484966417109,7824985701013143,652582573442231733,
%U A380917 59509330659228595239,5890961096785803165129,629159786981753244521787,72111288184913038638092337,8828896697592792281849882547
%N A380917 E.g.f. A(x) satisfies A(x) = exp(3 * x / (1 - x*A(x))) / (1 - x*A(x)).
%F A380917 a(n) = n! * Sum_{k=0..n} 3^k * (n-k+1)^(k-1) * binomial(2*n-k,n-k)/k!.
%o A380917 (PARI) a(n, q=3, r=3, s=0, t=1, u=1/3) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial((r*u+1)*n+((s-r)*u+t-1)*k+q*u-1, n-k)/k!);
%Y A380917 Cf. A380914, A380916.
%K A380917 nonn
%O A380917 0,2
%A A380917 _Seiichi Manyama_, Feb 08 2025