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 A370940 #10 Mar 06 2024 07:16:05
%S A370940 1,2,14,184,3612,94968,3139088,125181936,5851551680,313874206656,
%T A370940 19006905318528,1282738818650496,95477483835672960,
%U A370940 7770589670409684480,686519279618695022592,65436589709543394150912,6693486627002144059422720,731378220534326743907266560
%N A370940 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - 2*log(1+x)) ).
%H A370940 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A370940 a(n) = (1/(n+1)!) * Sum_{k=0..n} 2^k * (n+k)! * Stirling1(n,k).
%F A370940 a(n) ~ LambertW(exp(1/2))^n * n^(n-1) / (sqrt(1 + LambertW(exp(1/2))) * 2^(n+1) * exp(n) * (1 - LambertW(exp(1/2)))^(2*n+1)). - _Vaclav Kotesovec_, Mar 06 2024
%o A370940 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-2*log(1+x)))/x))
%o A370940 (PARI) a(n) = sum(k=0, n, 2^k*(n+k)!*stirling(n, k, 1))/(n+1)!;
%Y A370940 Cf. A258922, A370941.
%K A370940 nonn
%O A370940 0,2
%A A370940 _Seiichi Manyama_, Mar 06 2024