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 A380643 #19 Mar 16 2025 10:09:08
%S A380643 1,1,19,865,63289,6402421,827951491,130454402149,24246255965905,
%T A380643 5193341198368489,1259626725043888051,341256073037890028041,
%U A380643 102138911537774675080969,33470594059698797005874845,11918817613356955871120346979,4582850483720783516657005897741
%N A380643 Expansion of e.g.f. exp(x*G(3*x)^3) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
%F A380643 a(n) = 3 * n! * Sum_{k=0..n-1} 3^k * binomial(3*n+k,k)/((3*n+k) * (n-k-1)!) for n > 0.
%F A380643 E.g.f. A(x) satisfies x = log(A(x)) * (1 - 3*log(A(x)))^3.
%F A380643 a(n) = 3^(n-1)*U(1-n, 2-4*n, 1/3), where U is the Tricomi confluent hypergeometric function. - _Stefano Spezia_, Jan 29 2025
%F A380643 E.g.f.: exp( Series_Reversion( x*(1-3*x)^3 ) ). - _Seiichi Manyama_, Mar 16 2025
%o A380643 (PARI) a(n) = if(n==0, 1, 3*n!*sum(k=0, n-1, 3^k*binomial(3*n+k, k)/((3*n+k)*(n-k-1)!)));
%Y A380643 Cf. A002293, A380637.
%Y A380643 Cf. A080893, A380640.
%K A380643 nonn
%O A380643 0,3
%A A380643 _Seiichi Manyama_, Jan 29 2025