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 A371115 #11 Mar 11 2024 05:58:59
%S A371115 1,0,2,3,28,185,1566,18277,218744,3206961,52134490,935303501,
%T A371115 18733723812,406458491881,9598660337462,244471271572725,
%U A371115 6671672053304176,194631575264393057,6036199529439919410,198427339307102272669,6892068588221322730460
%N A371115 E.g.f. satisfies A(x) = 1 + x*(exp(x*A(x)) - 1).
%F A371115 a(n) = n! * Sum_{k=0..floor(n/2)} Stirling2(n-k,k)/(n-2*k+1)!.
%F A371115 From _Vaclav Kotesovec_, Mar 11 2024: (Start)
%F A371115 E.g.f.: 1 - x - LambertW(-exp((1 - x)*x)*x^2)/x.
%F A371115 a(n) ~ sqrt(2 + r - 2*r^2) * n^(n-1) / (exp(n) * r^(n+1)), where r = 0.5356007344755967412570670018666980389185523835846... if the root of the equation exp(1 + r - r^2) * r^2 = 1. (End)
%t A371115 nmax = 20; CoefficientList[Series[1 - x - ProductLog[-E^((1 - x)*x)*x^2]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Mar 11 2024 *)
%o A371115 (PARI) a(n) = n!*sum(k=0, n\2, stirling(n-k, k, 2)/(n-2*k+1)!);
%Y A371115 Cf. A000272, A371116.
%Y A371115 Cf. A371117.
%K A371115 nonn
%O A371115 0,3
%A A371115 _Seiichi Manyama_, Mar 11 2024