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 A380513 #11 Jan 26 2025 09:06:49
%S A380513 1,1,3,31,649,20241,831691,42281023,2558247441,179401012129,
%T A380513 14301145772371,1276863732880671,126200478678828313,
%U A380513 13677209933635675441,1612657716714084149019,205505541279096688937791,28144314031348292162103841,4122178445898981809990411073,642961375302043479923591655331
%N A380513 Expansion of e.g.f. exp(x*G(x)) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
%F A380513 a(n) = n! * Sum_{k=0..n-1} binomial(n+3*k,k)/((n+3*k) * (n-k-1)!) for n > 0.
%o A380513 (PARI) a(n) = if(n==0, 1, n!*sum(k=0, n-1, binomial(n+3*k, k)/((n+3*k)*(n-k-1)!)));
%Y A380513 Cf. A002293, A380514, A380515, A380516.
%Y A380513 Cf. A000262, A080893, A251569.
%K A380513 nonn
%O A380513 0,3
%A A380513 _Seiichi Manyama_, Jan 26 2025