A038057 a(n) = 2^n*n^(n-1).

2, 8, 72, 1024, 20000, 497664, 15059072, 536870912, 22039921152, 1024000000000, 53119845582848, 3043362286338048, 190857913323364352, 13004222844995895296, 956593800000000000000, 75557863725914323419136

Offset: 1

Author

Christian G. Bower, Jan 04 1999

Keywords

• nonn

Comments

Labeled rooted trees with n 2-colored nodes.

Links

• Index entries for sequences related to rooted trees

Crossrefs

Cf. A000169, A019762 (2*e), A038055-A038062.

Equals 2 * A052746(n).

Programs

Mathematica

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
(* or *)
nn=16;Drop[Range[0,nn]!CoefficientList[Series[-LambertW[-2x],{x,0,nn}],x],1]
(* or *)
Table[2^n*n^(n-1),{n,1,16}]  (* Geoffrey Critzer, Mar 17 2013 *)

Formula

E.g.f.: B(2*x) where B(x) is e.g.f. of A000169.

Limit_{n->oo} a(n+1)/(n*a(n)) = 2*e. - Stefano Spezia, Mar 12 2023

Extensions

New description from Vladeta Jovovic, Mar 08 2003