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 A370987 #10 Mar 07 2024 01:31:18
%S A370987 1,0,0,1,4,10,100,1295,11256,110964,1713720,27147285,409295260,
%T A370987 7192099486,146953847404,3083283003255,67579239087920,
%U A370987 1632183291677800,42282787050941616,1140103579166365929,32452333261311639540,982975683671186407090,31244119064026146137860
%N A370987 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^3/6*exp(x)) ).
%H A370987 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A370987 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} k^(n-3*k) * (n+k)!/(6^k * k! * (n-3*k)!).
%o A370987 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^3/6*exp(x)))/x))
%o A370987 (PARI) a(n) = sum(k=0, n\3, k^(n-3*k)*(n+k)!/(6^k*k!*(n-3*k)!))/(n+1);
%Y A370987 Cf. A213644, A370986.
%Y A370987 Cf. A346889, A370931.
%K A370987 nonn
%O A370987 0,5
%A A370987 _Seiichi Manyama_, Mar 06 2024