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 A370936 #15 Apr 20 2025 12:33:44
%S A370936 1,1,2,8,48,384,3872,47088,671360,10985088,202927872,4178030592,
%T A370936 94874787840,2355758714880,63498696376320,1846607063998464,
%U A370936 57630620308930560,1921296165774950400,68145277700464312320,2562234152415762972672,101801592691389968154624
%N A370936 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - log(1+2*x)/2) ).
%H A370936 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A370936 a(n) = (1/(n+1)!) * Sum_{k=0..n} 2^(n-k) * (n+k)! * Stirling1(n,k).
%F A370936 a(n) ~ 2^(2*n + 1) * LambertW(exp(-1))^n * n^(n-1) / (sqrt(1 + LambertW(exp(-1))) * exp(n) * (1 - LambertW(exp(-1)))^(2*n + 1)). - _Vaclav Kotesovec_, Mar 06 2024
%t A370936 a[n_]:=Sum[2^(n-k)*(n+k)!*StirlingS1[n, k],{k,0,n}]/(n+1)!; Array[a,21,0] (* _Stefano Spezia_, Apr 20 2025 *)
%o A370936 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-log(1+2*x)/2))/x))
%o A370936 (PARI) a(n) = sum(k=0, n, 2^(n-k)*(n+k)!*stirling(n, k, 1))/(n+1)!;
%Y A370936 Cf. A198860, A370937.
%K A370936 nonn
%O A370936 0,3
%A A370936 _Seiichi Manyama_, Mar 06 2024