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 A370909 #11 Nov 07 2024 15:41:54
%S A370909 1,2,14,174,3174,76902,2331630,85048686,3629630070,177523551990,
%T A370909 9793095667326,601667773414974,40747538527887366,3016185673617546822,
%U A370909 242280567558408368142,20991011860150103490318,1951271511259385883645846,193723174296061459833879702
%N A370909 Expansion of e.g.f. (1/x) * Series_Reversion( 3*x/(1 + 2*exp(3*x)) ).
%H A370909 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A370909 a(n) = 1/(3*(n+1)) * Sum_{k=0..n+1} 2^k * k^n * binomial(n+1,k).
%F A370909 a(n) = n! * Sum_{k=0..n} 2^k * 3^(n-k) * Stirling2(n,k)/(n-k+1)!. - _Seiichi Manyama_, Nov 07 2024
%o A370909 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(3*x/(1+2*exp(3*x)))/x))
%o A370909 (PARI) a(n) = sum(k=0, n+1, 2^k*k^n*binomial(n+1, k))/(3*(n+1));
%Y A370909 Cf. A201595, A370910.
%K A370909 nonn
%O A370909 0,2
%A A370909 _Seiichi Manyama_, Mar 05 2024