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 A370907 #13 Nov 07 2024 15:41:47
%S A370907 1,1,5,42,519,8526,175329,4338594,125632035,4169652390,156101072373,
%T A370907 6508965708378,299190004799679,15031796956994286,819581031710623017,
%U A370907 48199003176462356754,3041324249730311069595,204962505644116505863926
%N A370907 Expansion of e.g.f. (1/x) * Series_Reversion( 3*x/(2 + exp(3*x)) ).
%H A370907 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A370907 a(n) = 1/(3*(n+1)) * Sum_{k=0..n+1} 2^(n+1-k) * k^n * binomial(n+1,k).
%F A370907 a(n) = n! * Sum_{k=0..n} 3^(n-k) * Stirling2(n,k)/(n-k+1)!. - _Seiichi Manyama_, Nov 07 2024
%o A370907 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(3*x/(2+exp(3*x)))/x))
%o A370907 (PARI) a(n) = sum(k=0, n+1, 2^(n+1-k)*k^n*binomial(n+1, k))/(3*(n+1));
%Y A370907 Cf. A201595, A370908.
%K A370907 nonn
%O A370907 0,3
%A A370907 _Seiichi Manyama_, Mar 05 2024