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 A380780 #15 Feb 03 2025 11:08:56
%S A380780 1,3,27,436,10353,326856,12920731,614694816,34223383809,2184028353280,
%T A380780 157223422977531,12606338448248832,1114292924502666673,
%U A380780 107657947282494206976,11287975339133863810875,1276603658863119005618176,154909721707963344338403969,20076669149268201122957819904
%N A380780 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * (1 + x)) / (1 + x)^2 ).
%H A380780 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A380780 E.g.f. A(x) satisfies A(x) = exp( x * A(x) * (1 + x*A(x)) ) * (1 + x*A(x))^2.
%F A380780 a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(2*n+k+2,n-k)/k!.
%o A380780 (PARI) a(n, q=1, r=1, s=1, t=1, 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 A380780 Cf. A377829, A380778, A380779, A380781.
%Y A380780 Cf. A380665.
%K A380780 nonn
%O A380780 0,2
%A A380780 _Seiichi Manyama_, Feb 02 2025