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 A371019 #10 Mar 08 2024 07:59:55
%S A371019 1,0,0,6,24,60,2280,35490,322896,6532344,175392720,3351681630,
%T A371019 74021715240,2328376978356,68824597123464,1989994550546730,
%U A371019 69687384248405280,2634948077918611440,98220733842576688416,3966108617957749165494,175679596523004500742840
%N A371019 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x^3*exp(x)) ).
%H A371019 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A371019 a(n) = (n!/(n+1)) * Sum_{k=0..floor(n/3)} k^(n-3*k) * binomial(n+1,k)/(n-3*k)!.
%o A371019 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1+x^3*exp(x)))/x))
%o A371019 (PARI) a(n) = n!*sum(k=0, n\3, k^(n-3*k)*binomial(n+1, k)/(n-3*k)!)/(n+1);
%Y A371019 Cf. A161633, A371018.
%Y A371019 Cf. A365287.
%K A371019 nonn
%O A371019 0,4
%A A371019 _Seiichi Manyama_, Mar 08 2024