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 A380919 #9 Feb 08 2025 10:29:47
%S A380919 1,4,55,1380,51213,2533968,157230099,11752365600,1028673637785,
%T A380919 103250018926080,11693974366638639,1475530063767972864,
%U A380919 205281631888995454245,31221155498006896773120,5153702313885813394180875,917695970480270443222536192,175344823710094148613399084849
%N A380919 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x) * exp(-3*x/(1 - x)) ).
%H A380919 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A380919 E.g.f. A(x) satisfies A(x) = exp(3*x*A(x) / (1 - x*A(x))) / (1 - x*A(x)).
%F A380919 a(n) = n! * Sum_{k=0..n} 3^k * (n+1)^(k-1) * binomial(2*n,n-k)/k!.
%o A380919 (PARI) a(n, q=3, r=3, s=3, t=1, u=1/3) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial((r*u+1)*n+((s-r)*u+t-1)*k+q*u-1, n-k)/k!);
%Y A380919 Cf. A380663, A380918.
%Y A380919 Cf. A380917.
%K A380919 nonn
%O A380919 0,2
%A A380919 _Seiichi Manyama_, Feb 08 2025