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A038057
a(n) = 2^n*n^(n-1).
4
2, 8, 72, 1024, 20000, 497664, 15059072, 536870912, 22039921152, 1024000000000, 53119845582848, 3043362286338048, 190857913323364352, 13004222844995895296, 956593800000000000000, 75557863725914323419136
OFFSET
1,1
COMMENTS
Labeled rooted trees with n 2-colored nodes.
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
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 *)
CROSSREFS
Equals 2 * A052746(n).
Sequence in context: A364408 A194499 A009478 * A107270 A294351 A342177
KEYWORD
nonn
AUTHOR
Christian G. Bower, Jan 04 1999
EXTENSIONS
New description from Vladeta Jovovic, Mar 08 2003
STATUS
approved