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 A371007 #14 Nov 07 2024 15:42:02
%S A371007 1,3,24,336,6864,185808,6286560,255703584,12163234560,662866302720,
%T A371007 40735968170496,2787616114300416,210253334027606016,
%U A371007 17331011952028981248,1550159522438672412672,149539908497083261980672,15476976326308703371984896
%N A371007 Expansion of e.g.f. (1/x) * Series_Reversion( 2*x/(3*exp(2*x) - 1) ).
%H A371007 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A371007 a(n) = 1/(2*(n+1)) * Sum_{k=0..n+1} 3^k * (-1)^(n+1-k) * k^n * binomial(n+1,k).
%F A371007 a(n) = n! * Sum_{k=0..n} 3^k * 2^(n-k) * Stirling2(n,k)/(n-k+1)!. - _Seiichi Manyama_, Nov 07 2024
%o A371007 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(2*x/(3*exp(2*x)-1))/x))
%o A371007 (PARI) a(n) = sum(k=0, n+1, 3^k*(-1)^(n+1-k)*k^n*binomial(n+1, k))/(2*(n+1));
%Y A371007 Cf. A371005.
%K A371007 nonn
%O A371007 0,2
%A A371007 _Seiichi Manyama_, Mar 08 2024