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 A380781 #16 Feb 03 2025 11:08:33
%S A380781 1,3,29,514,13473,470616,20607781,1086800352,67105960641,
%T A380781 4750972007680,379512594172941,33771911612182272,3313441417839023521,
%U A380781 355371388642280715264,41365962922892138767125,5193995331631149377867776,699785874809076112607739009,100701968551637581411176480768
%N A380781 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * (1 + x)^2) / (1 + x)^2 ).
%H A380781 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A380781 E.g.f. A(x) satisfies A(x) = exp( x * A(x) * (1 + x*A(x))^2 ) * (1 + x*A(x))^2.
%F A380781 a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(2*n+2*k+2,n-k)/k!.
%o A380781 (PARI) a(n, q=1, r=1, s=1, t=2, u=2) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial(r*u*n+((s-r)*u+t)*k+q*u, n-k)/k!);
%Y A380781 Cf. A377829, A380778, A380779, A380780.
%Y A380781 Cf. A365031, A380762.
%Y A380781 Cf. A380666.
%K A380781 nonn
%O A380781 0,2
%A A380781 _Seiichi Manyama_, Feb 02 2025