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 A371006 #13 Nov 07 2024 10:54:33
%S A371006 1,3,21,246,4143,91938,2543457,84476766,3278575515,145703001450,
%T A371006 7299102908613,407061606983430,25016221521245703,1679926053870309378,
%U A371006 122399565517464024009,9617404242454811783598,810684382032520533507891,72976185712308646408856538
%N A371006 Expansion of e.g.f. (1/x) * Series_Reversion( x/(3*exp(x) - 2) ).
%H A371006 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A371006 a(n) = 1/(n+1) * Sum_{k=0..n+1} 3^k * (-2)^(n+1-k) * k^n * binomial(n+1,k).
%F A371006 a(n) = n! * Sum_{k=0..n} 3^k * Stirling2(n,k)/(n-k+1)!. - _Seiichi Manyama_, Nov 07 2024
%o A371006 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(3*exp(x)-2))/x))
%o A371006 (PARI) a(n) = sum(k=0, n+1, 3^k*(-2)^(n+1-k)*k^n*binomial(n+1, k))/(n+1);
%Y A371006 Cf. A000272, A371005.
%Y A371006 Cf. A371007.
%K A371006 nonn
%O A371006 0,2
%A A371006 _Seiichi Manyama_, Mar 08 2024