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 A349598 #24 Nov 26 2021 08:48:19
%S A349598 1,1,6,71,1279,31142,958127,35674921,1560207964,78410153193,
%T A349598 4453247964775,282086867840252,19718661737739301,1507855981764016549,
%U A349598 125211854842018500134,11220898483255456505555,1079389691811367897870339,110936313685240067472613726
%N A349598 E.g.f. satisfies: log(A(x)) = exp(x*A(x)^2) - 1.
%H A349598 Seiichi Manyama, <a href="/A349598/b349598.txt">Table of n, a(n) for n = 0..343</a>
%F A349598 a(n) = Sum_{k=0..n} (2*n+1)^(k-1) * Stirling2(n,k).
%F A349598 a(n) ~ s * n^(n-1) / (2 * sqrt(1 + r*s^2) * exp(n) * r^n), where r = 0.1513832219344136560178112221696108323993292386502... and s = 1.52429184135463908701026733917578550814344591549... are roots of the system of equations (1 + log(s))*2*r*s^2 = 1, 2*r*s^2*exp(r*s^2) = 1. - _Vaclav Kotesovec_, Nov 25 2021
%F A349598 Equivalently, a(n) ~ n^(n-1) / (2*sqrt(1 + LambertW(1/2)) * LambertW(1/2)^n * exp(3*n + 1 - (n + 1/2)/LambertW(1/2))). - _Vaclav Kotesovec_, Nov 26 2021
%t A349598 a[n_] := Sum[(2*n + 1)^(k - 1)*StirlingS2[n, k], {k, 0, n}]; Array[a, 18, 0] (* _Amiram Eldar_, Nov 23 2021 *)
%o A349598 (PARI) a(n) = sum(k=0, n, (2*n+1)^(k-1)*stirling(n, k, 2));
%Y A349598 Cf. A001761, A001763, A349599.
%Y A349598 Cf. A349524, A349601.
%K A349598 nonn
%O A349598 0,3
%A A349598 _Seiichi Manyama_, Nov 22 2021