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 A357424 #16 Sep 09 2024 09:34:14
%S A357424 0,1,1,4,21,156,1470,16843,227367,3533974,62163477,1220852524,
%T A357424 26480355110,628693388909,16216901961481,451609382251836,
%U A357424 13504072800481613,431544662700594212,14677503631085378170,529370720888418692643,20180856622352239827687
%N A357424 E.g.f. satisfies A(x) * exp(A(x)) = exp(x * exp(A(x))) - 1.
%H A357424 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A357424 a(n) = Sum_{k=1..n} (n-k)^(k-1) * Stirling2(n,k).
%F A357424 a(n) ~ n^(n-1) * (1 + exp(s)*s)^(n + 1/2) / (sqrt(exp(s)*(1 + s + s^2) - 1) * exp(n) * (1 + s)^(n - 1/2)), where s = 1.104072744884035178291292242554731... is the root of the equation 1 + s = (exp(-s) + s) * log(1 + exp(s)*s). - _Vaclav Kotesovec_, Nov 14 2022
%F A357424 E.g.f.: Series_Reversion( exp(-x) * log(1 + x * exp(x)) ). - _Seiichi Manyama_, Sep 09 2024
%t A357424 Join[{0,1},Table[Sum[(n-k)^(k-1) * StirlingS2[n,k], {k,1,n}], {n,2,20}]] (* _Vaclav Kotesovec_, Nov 14 2022 *)
%o A357424 (PARI) a(n) = sum(k=1, n, (n-k)^(k-1)*stirling(n, k, 2));
%Y A357424 Cf. A052888, A357346, A357347, A357348.
%Y A357424 Cf. A349588.
%K A357424 nonn
%O A357424 0,4
%A A357424 _Seiichi Manyama_, Sep 27 2022