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 A370989 #16 Mar 07 2024 01:31:41
%S A370989 1,0,0,6,12,20,2910,22722,117656,8482392,143398170,1519998590,
%T A370989 79655138772,2206506673956,39101112995126,1798446230741370,
%U A370989 68667380639283120,1795441154500375472,81344029377887798706,3830461514154681289974,135388937631209203030700
%N A370989 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^2*(exp(x) - 1)) ).
%H A370989 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A370989 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (n+k)! * Stirling2(n-2*k,k)/(n-2*k)!.
%o A370989 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^2*(exp(x)-1)))/x))
%o A370989 (PARI) a(n) = sum(k=0, n\3, (n+k)!*stirling(n-2*k, k, 2)/(n-2*k)!)/(n+1);
%Y A370989 Cf. A052894, A370988, A370990.
%Y A370989 Cf. A358013.
%K A370989 nonn
%O A370989 0,4
%A A370989 _Seiichi Manyama_, Mar 06 2024