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 A380916 #8 Feb 08 2025 10:29:59
%S A380916 1,3,20,254,4832,123152,3947008,152638320,6919663360,359984690432,
%T A380916 21143150157824,1384004213748224,99919253031411712,
%U A380916 7887827865170055168,675952599490594422784,62495398874421426649088,6200786173880446466785280,657212589119205105944428544
%N A380916 E.g.f. A(x) satisfies A(x) = exp(2 * x / (1 - x*A(x))) / (1 - x*A(x)).
%F A380916 a(n) = n! * Sum_{k=0..n} 2^k * (n-k+1)^(k-1) * binomial(2*n-k,n-k)/k!.
%o A380916 (PARI) a(n, q=2, r=2, s=0, t=1, u=1/2) = 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 A380916 Cf. A380914, A380917.
%K A380916 nonn
%O A380916 0,2
%A A380916 _Seiichi Manyama_, Feb 08 2025