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 A371117 #12 Mar 11 2024 05:35:42
%S A371117 1,0,2,3,32,210,2184,26460,373344,6150816,113958720,2362345920,
%T A371117 54094694400,1355708296800,36926213869440,1085886303989760,
%U A371117 34291129916574720,1157362522046277120,41576054625791078400,1583864892141097098240,63779322541075124428800
%N A371117 E.g.f. satisfies A(x) = 1 - x*log(1 - x*A(x)).
%F A371117 a(n) = n! * Sum_{k=0..floor(n/2)} |Stirling1(n-k,k)|/(n-2*k+1)!.
%F A371117 a(n) ~ sqrt(2 - r*(2*r+1)) * n^(n-1) / (exp(n) * r^n), where r = 0.4599065470184992266076522060382204730855199647380... is the root of the equation 1/r + 2*r*log(r) = 1+r. - _Vaclav Kotesovec_, Mar 11 2024
%t A371117 nmax = 20; A[_] = 0; Do[A[x_] = 1 - x*Log[1 - x*A[x]] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] * Range[0,nmax]! (* _Vaclav Kotesovec_, Mar 11 2024 *)
%o A371117 (PARI) a(n) = n!*sum(k=0, n\2, abs(stirling(n-k, k, 1))/(n-2*k+1)!);
%Y A371117 Cf. A138013, A371118.
%Y A371117 Cf. A371115.
%K A371117 nonn
%O A371117 0,3
%A A371117 _Seiichi Manyama_, Mar 11 2024