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 A380646 #13 Feb 06 2025 09:01:29
%S A380646 1,4,46,932,27568,1080432,52916176,3115326496,214470890496,
%T A380646 16914853191680,1504252282653184,148956086481767424,
%U A380646 16256865070022066176,1938988214539948730368,250943399365390735104000,35026523834624205803491328,5245178283068781060488298496,838841884254236846183525646336
%N A380646 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-2*x)/(1 + x)^2 ).
%H A380646 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A380646 E.g.f. A(x) satisfies A(x) = (1 + x*A(x))^2 * exp(2 * x * A(x)).
%F A380646 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377892.
%F A380646 a(n) = 2 * n! * Sum_{k=0..n} (2*n+2)^(k-1) * binomial(2*n+2,n-k)/k!.
%t A380646 nmax=18; CoefficientList[(1/x)InverseSeries[Series[x*Exp[-2*x]/(1 + x)^2 ,{x,0,nmax}]],x]Range[0,nmax-1]! (* _Stefano Spezia_, Feb 06 2025 *)
%o A380646 (PARI) a(n) = 2*n!*sum(k=0, n, (2*n+2)^(k-1)*binomial(2*n+2, n-k)/k!);
%Y A380646 Cf. A088690, A380647, A380648.
%Y A380646 Cf. A065866, A377829.
%Y A380646 Cf. A097629, A380828.
%Y A380646 Cf. A377892.
%K A380646 nonn
%O A380646 0,2
%A A380646 _Seiichi Manyama_, Feb 06 2025