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 A217061 #20 Feb 08 2025 20:23:04
%S A217061 1,1,3,15,109,1053,12767,186763,3204313,63128665,1404963387,
%T A217061 34867190823,954800951749,28600649870133,930325531322519,
%U A217061 32658109219519843,1230609634110271921,49545182501048868145,2122562841050605554291,96411483206025310956735,4628163318874435745244445
%N A217061 Expansion of e.g.f. exp(A006351(x)).
%F A217061 a(n) = sum(m=1..n, (sum(k=0..n-m, (n+k-1)!*sum(j=0..k, 1/(k-j)!*sum(l=0..j, (2^(j-l)*(-1)^(l+j)*Stirling1(n-m-l+j,j-l))/(l!*(n-m-l+j)!)))))/(m-1)!), n>0, a(0)=1.
%F A217061 From _Vaclav Kotesovec_, Aug 04 2014: (Start)
%F A217061 E.g.f.: 4*LambertW(-exp((x-1)/2)/2)^2 / exp(x).
%F A217061 a(n) ~ sqrt(2) * n^(n-1) / (exp(n-1) * (2*log(2)-1)^(n-1/2)). (End)
%t A217061 CoefficientList[Series[4*ProductLog[-E^((x-1)/2)/2]^2/E^x,{x, 0, 15}], x]*Range[0, 15]! (* _Vaclav Kotesovec_, Aug 04 2014 *)
%o A217061 (Maxima)
%o A217061 a(n):=(sum((m*sum((n+k-1)!*sum(1/(k-j)!*sum((2^(j-l)*(-1)^(l+j)*stirling1(n-m-l+j,j-l))/(l!*(n-m-l+j)!),l,0,j),j,0,k),k,0,n-m))/m!,m,1,n));
%o A217061 (PARI) my(x='x+O('x^20)); apply(round, Vec(serlaplace(4*lambertw(-exp((x-1)/2)/2)^2 / exp(x)))) \\ _Michel Marcus_, Jan 27 2025
%Y A217061 Cf. A006351, A379458.
%K A217061 nonn
%O A217061 0,3
%A A217061 _Vladimir Kruchinin_, Sep 26 2012
%E A217061 More terms from _Michel Marcus_, Jan 27 2025