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 A380511 #22 Mar 15 2025 09:43:28
%S A380511 1,1,5,55,961,23141,711421,26631235,1175535425,59786520841,
%T A380511 3442729157461,221413508687471,15730688410899265,1223574846548300845,
%U A380511 103417508018836074701,9437941200860641295611,924934291227615821904001,96881241931552168636182545,10801002623361396194857667365
%N A380511 Expansion of e.g.f. exp(x*G(x)^2) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764.
%F A380511 a(n) = 2 * n! * Sum_{k=0..n-1} binomial(2*n+k,k)/((2*n+k) * (n-k-1)!) for n > 0.
%F A380511 a(n) = U(1-n, 2-3*n, 1), where U is the Tricomi confluent hypergeometric function. - _Stefano Spezia_, Jan 26 2025
%F A380511 E.g.f.: exp( Series_Reversion( x*(1-x)^2 ) ). - _Seiichi Manyama_, Mar 15 2025
%o A380511 (PARI) a(n) = if(n==0, 1, 2*n!*sum(k=0, n-1, binomial(2*n+k, k)/((2*n+k)*(n-k-1)!)));
%Y A380511 Cf. A251569, A380512.
%Y A380511 Cf. A080893, A380515.
%Y A380511 Cf. A082579, A251568, A380514.
%Y A380511 Cf. A001764, A006013, A370054, A382058.
%K A380511 nonn
%O A380511 0,3
%A A380511 _Seiichi Manyama_, Jan 26 2025