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 A371370 #12 Sep 10 2024 06:17:26
%S A371370 0,1,5,62,1246,34734,1239708,53958456,2771832656,164151829440,
%T A371370 11010949643640,825134834757936,68321156113803360,6194283782068848816,
%U A371370 610322188305019432032,64936303681095948453120,7419917758371561069774336,906217650382400588573066880
%N A371370 E.g.f. satisfies A(x) = -log(1 - x/(1 - A(x))^2).
%H A371370 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A371370 E.g.f.: Series_Reversion( (1 - x)^2 * (1 - exp(-x)) ).
%F A371370 a(n) = Sum_{k=1..n} (2*n+k-2)!/(2*n-1)! * |Stirling1(n,k)|.
%F A371370 a(n) ~ LambertW(2*exp(3))^n * n^(n-1) / (sqrt(2*(1 + LambertW(2*exp(3)))) * (LambertW(2*exp(3)) - 2)^(3*n-1) * exp(n)). - _Vaclav Kotesovec_, Sep 10 2024
%t A371370 Table[Sum[(2*n+k-2)!/(2*n-1)! * Abs[StirlingS1[n,k]], {k,1,n}], {n,0,20}] (* _Vaclav Kotesovec_, Sep 10 2024 *)
%o A371370 (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(serreverse((1-x)^2*(1-exp(-x))))))
%o A371370 (PARI) a(n) = sum(k=1, n, (2*n+k-2)!/(2*n-1)!*abs(stirling(n, k, 1)));
%Y A371370 Cf. A368033, A371371.
%Y A371370 Cf. A052842.
%K A371370 nonn
%O A371370 0,3
%A A371370 _Seiichi Manyama_, Mar 20 2024