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 A370894 #19 Mar 06 2024 11:43:29
%S A370894 1,1,6,64,1016,21576,575680,18525088,698625408,30229271680,
%T A370894 1476535180544,80371762466304,4824793854177280,316685993746640896,
%U A370894 22563822118152880128,1734427247284290015232,143072322233503079038976,12606854482934004152303616
%N A370894 Expansion of e.g.f. (1/x) * Series_Reversion( x*(3 - exp(2*x))/2 ).
%F A370894 a(n) = (1/(n+1)!) * Sum_{k=0..n} 2^(n-k) * (n+k)! * Stirling2(n,k).
%F A370894 a(n) ~ 2^(2*n+1) * LambertW(3*exp(1))^(n+1) * n^(n-1) / (sqrt(1 + LambertW(3*exp(1))) * 3^(n+1) * exp(n) * (LambertW(3*exp(1)) - 1)^(2*n+1)). - _Vaclav Kotesovec_, Mar 06 2024
%o A370894 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(3-exp(2*x))/2)/x))
%o A370894 (PARI) a(n) = sum(k=0, n, 2^(n-k)*(n+k)!*stirling(n, k, 2))/(n+1)!;
%Y A370894 Cf. A052894, A370934.
%Y A370894 Cf. A258922.
%K A370894 nonn
%O A370894 0,3
%A A370894 _Seiichi Manyama_, Mar 06 2024