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 A370876 #12 Mar 09 2024 08:16:06
%S A370876 1,1,2,12,120,1320,17640,304920,6249600,143579520,3711052800,
%T A370876 107762054400,3455138332800,120802387305600,4583177081683200,
%U A370876 187766031131078400,8256125218115174400,387662886088250572800,19364540503274942976000,1025507260911983244595200
%N A370876 Expansion of e.g.f. (1/x) * Series_Reversion( x/(x + exp(x^3)) ).
%H A370876 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A370876 a(n) = n! * Sum_{k=0..floor(n/3)} (3*k+1)^(k-1) * binomial(n,3*k)/k!.
%F A370876 E.g.f.: (LambertW( -3*x^3/(1-x)^3 ) / (-3*x^3))^(1/3).
%o A370876 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(x+exp(x^3)))/x))
%o A370876 (PARI) a(n) = n!*sum(k=0, n\3, (3*k+1)^(k-1)*binomial(n, 3*k)/k!);
%Y A370876 Cf. A352410, A370875.
%Y A370876 Cf. A360609.
%K A370876 nonn
%O A370876 0,3
%A A370876 _Seiichi Manyama_, Mar 03 2024