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 A380515 #19 Mar 15 2025 09:43:35
%S A380515 1,1,7,109,2689,91261,3950191,208064137,12917499169,923765042809,
%T A380515 74780847503191,6760168138392901,675023676995501857,
%U A380515 73787463232202560309,8763902701210982610559,1123850728979698205132641,154757223522414820829369281,22775744033825102490806751217
%N A380515 Expansion of e.g.f. exp(x*G(x)^3) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
%F A380515 a(n) = 3 * n! * Sum_{k=0..n-1} binomial(3*n+k,k)/((3*n+k) * (n-k-1)!) for n > 0.
%F A380515 a(n) = U(1-n, 2-4*n, 1), where U is the Tricomi confluent hypergeometric function. - _Stefano Spezia_, Jan 26 2025
%F A380515 E.g.f.: exp( Series_Reversion( x*(1-x)^3 ) ). - _Seiichi Manyama_, Mar 15 2025
%o A380515 (PARI) a(n) = if(n==0, 1, 3*n!*sum(k=0, n-1, binomial(3*n+k, k)/((3*n+k)*(n-k-1)!)));
%Y A380515 Cf. A380513, A380514, A380516.
%Y A380515 Cf. A080893, A380511.
%Y A380515 Cf. A091695, A250917, A380512.
%Y A380515 Cf. A002293, A006632, A370057, A382059.
%K A380515 nonn
%O A380515 0,3
%A A380515 _Seiichi Manyama_, Jan 26 2025