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 A370985 #9 Mar 07 2024 01:30:58
%S A370985 1,0,0,6,24,60,3000,45570,403536,10644984,297562320,5517833310,
%T A370985 142801022760,5076208052916,150282366476424,4713707747551530,
%U A370985 189345734667052320,7517503455423740400,295622259241028433696,13370535071068474177974,642403497550155241197240
%N A370985 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^3*exp(x)) ).
%H A370985 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A370985 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} k^(n-3*k) * (n+k)!/(k! * (n-3*k)!).
%o A370985 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^3*exp(x)))/x))
%o A370985 (PARI) a(n) = sum(k=0, n\3, k^(n-3*k)*(n+k)!/(k!*(n-3*k)!))/(n+1);
%Y A370985 Cf. A213644, A370984.
%Y A370985 Cf. A358081, A370928.
%K A370985 nonn
%O A370985 0,4
%A A370985 _Seiichi Manyama_, Mar 06 2024