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 A038057 #26 Mar 14 2023 09:31:20
%S A038057 2,8,72,1024,20000,497664,15059072,536870912,22039921152,
%T A038057 1024000000000,53119845582848,3043362286338048,190857913323364352,
%U A038057 13004222844995895296,956593800000000000000,75557863725914323419136
%N A038057 a(n) = 2^n*n^(n-1).
%C A038057 Labeled rooted trees with n 2-colored nodes.
%H A038057 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A038057 E.g.f.: B(2*x) where B(x) is e.g.f. of A000169.
%F A038057 Limit_{n->oo} a(n+1)/(n*a(n)) = 2*e. - _Stefano Spezia_, Mar 12 2023
%t A038057 nn=16;f[x_]:=Sum[a[n]x^n/n!,{n,0,nn}];s=SolveAlways[0==Series[f[x]-2x Exp[f[x]],{x,0,nn}],x];Table[a[n],{n,1,nn}]/.s
%t A038057 (* or *)
%t A038057 nn=16;Drop[Range[0,nn]!CoefficientList[Series[-LambertW[-2x],{x,0,nn}],x],1]
%t A038057 (* or *)
%t A038057 Table[2^n*n^(n-1),{n,1,16}] (* _Geoffrey Critzer_, Mar 17 2013 *)
%Y A038057 Cf. A000169, A019762 (2*e), A038055-A038062.
%Y A038057 Equals 2 * A052746(n).
%K A038057 nonn
%O A038057 1,1
%A A038057 _Christian G. Bower_, Jan 04 1999
%E A038057 New description from _Vladeta Jovovic_, Mar 08 2003