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 A380647 #15 Feb 06 2025 09:01:21
%S A380647 1,6,105,3246,146637,8780688,657224901,59140486800,6223651526457,
%T A380647 750357182131200,102014741343847329,15443915464974191616,
%U A380647 2576937457466957107845,469914373917914931984384,92982800086882512621716925,19843243096453465663599962112,4543276116844426827394718716401
%N A380647 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-3*x)/(1 + x)^3 ).
%H A380647 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A380647 E.g.f. A(x) satisfies A(x) = (1 + x*A(x))^3 * exp(3 * x * A(x)).
%F A380647 E.g.f.: B(x)^3, where B(x) is the e.g.f. of A377893.
%F A380647 a(n) = 3 * n! * Sum_{k=0..n} (3*n+3)^(k-1) * binomial(3*n+3,n-k)/k!.
%t A380647 nmax=17; CoefficientList[(1/x)InverseSeries[Series[x*Exp[-3*x]/(1 + x)^3 ,{x,0,nmax}]],x]Range[0,nmax-1]! (* _Stefano Spezia_, Feb 06 2025 *)
%o A380647 (PARI) a(n) = 3*n!*sum(k=0, n, (3*n+3)^(k-1)*binomial(3*n+3, n-k)/k!);
%Y A380647 Cf. A088690, A380646, A380648.
%Y A380647 Cf. A370055, A377830.
%Y A380647 Cf. A377893.
%K A380647 nonn
%O A380647 0,2
%A A380647 _Seiichi Manyama_, Feb 06 2025