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 A371021 #12 Aug 05 2025 12:17:01
%S A371021 1,0,0,1,4,10,80,1015,9016,80724,1092120,16872405,246966940,
%T A371021 3932454526,73869476044,1485097614455,30688224287280,682450482838440,
%U A371021 16508839426673136,420562937260614249,11193327347979937140,315276822746559147250,9383980947735649740100
%N A371021 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x^3/6*exp(x)) ).
%H A371021 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A371021 a(n) = (n!/(n+1)) * Sum_{k=0..floor(n/3)} k^(n-3*k) * binomial(n+1,k)/(6^k * (n-3*k)!).
%t A371021 Join[{1}, Table[(n!/(n + 1))*Sum[k^(n - 3*k)*Binomial[n + 1, k]/(6^k*(n - 3*k)!), {k, 0, Floor[n/3]}], {n, 30}]] (* _Wesley Ivan Hurt_, Aug 05 2025 *)
%o A371021 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1+x^3/6*exp(x)))/x))
%o A371021 (PARI) a(n) = n!*sum(k=0, n\3, k^(n-3*k)*binomial(n+1, k)/(6^k*(n-3*k)!))/(n+1);
%Y A371021 Cf. A370926, A371019.
%K A371021 nonn
%O A371021 0,5
%A A371021 _Seiichi Manyama_, Mar 08 2024