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A038057 a(n) = 2^n*n^(n-1). 3
2, 8, 72, 1024, 20000, 497664, 15059072, 536870912, 22039921152, 1024000000000, 53119845582848, 3043362286338048, 190857913323364352, 13004222844995895296, 956593800000000000000, 75557863725914323419136 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Labeled rooted trees with n 2-colored nodes.

LINKS

Table of n, a(n) for n=1..16.

Index entries for sequences related to rooted trees

FORMULA

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

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

Cf. A000169, A038055-A038062.

Equals 2 * A052746(n).

Sequence in context: A060635 A194499 A009478 * A107270 A294351 A342177

Adjacent sequences:  A038054 A038055 A038056 * A038058 A038059 A038060

KEYWORD

nonn

AUTHOR

Christian G. Bower, Jan 04 1999

EXTENSIONS

New description from Vladeta Jovovic, Mar 08 2003

STATUS

approved

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Last modified January 20 01:18 EST 2022. Contains 350467 sequences. (Running on oeis4.)