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 A380648 #14 Feb 06 2025 10:23:03
%S A380648 1,8,188,7816,475096,38289504,3857806144,467330651456,66209818738176,
%T A380648 10747317030192640,1967261819870112256,400989528160028255232,
%U A380648 90087157573721153554432,22119056538323287540637696,5893098619063477612068864000,1693364632974231188010697990144
%N A380648 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-4*x)/(1 + x)^4 ).
%H A380648 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A380648 E.g.f. A(x) satisfies A(x) = (1 + x*A(x))^4 * exp(4 * x * A(x)).
%F A380648 a(n) = 4 * n! * Sum_{k=0..n} (4*n+4)^(k-1) * binomial(4*n+4,n-k)/k!.
%t A380648 nmax=16; CoefficientList[(1/x)InverseSeries[Series[x*Exp[-4*x]/(1 + x)^4, {x, 0, nmax}]], x]Range[0, nmax-1]! (* _Stefano Spezia_, Feb 06 2025 *)
%o A380648 (PARI) a(n) = 4*n!*sum(k=0, n, (4*n+4)^(k-1)*binomial(4*n+4, n-k)/k!);
%Y A380648 Cf. A088690, A380646, A380647.
%Y A380648 Cf. A370058.
%K A380648 nonn
%O A380648 0,2
%A A380648 _Seiichi Manyama_, Feb 06 2025