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 A380514 #10 Jan 26 2025 09:06:37
%S A380514 1,1,5,67,1537,50021,2107021,108885295,6665443457,471522589417,
%T A380514 37843890892021,3397250515809371,337267132243022785,
%U A380514 36687625652474612557,4339368321317331858557,554467482301151809302151,76112537023512618262963201,11170667360636927554290623825,1745500813880455301486766050917
%N A380514 Expansion of e.g.f. exp(x*G(x)^2) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
%F A380514 a(n) = 2 * n! * Sum_{k=0..n-1} binomial(2*n+2*k,k)/((2*n+2*k) * (n-k-1)!) for n > 0.
%o A380514 (PARI) a(n) = if(n==0, 1, 2*n!*sum(k=0, n-1, binomial(2*n+2*k, k)/((2*n+2*k)*(n-k-1)!)));
%Y A380514 Cf. A002293, A069271, A380513, A380515, A380516.
%K A380514 nonn
%O A380514 0,3
%A A380514 _Seiichi Manyama_, Jan 26 2025