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A052317 Number of labeled trees with n nodes and 2-colored internal (non-leaf) nodes. 3
1, 1, 1, 6, 56, 730, 12372, 259574, 6511920, 190413234, 6364960940, 239556803662, 10028763883272, 462366507311306, 23282257730716740, 1271520006077859750, 74865320814990626912, 4727699146425478764898 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..17.

Index entries for sequences related to trees

FORMULA

E.g.f.: 1 + B(x) - x*B(x) - B(x)^2/2 where B(x) is g.f. of A052316.

a(n) ~ (1+LambertW(-exp(-1)/2))^(3/2) * n^(n-2) / (exp(n)*(-LambertW(-exp(-1)/2))^n). - Vaclav Kotesovec, Oct 05 2013

MATHEMATICA

CoefficientList[Series[1+(1-x)*(-x-LambertW[-2*x*E^(-x)])-(-x-LambertW[-2*x*E^(-x)])^2/2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 05 2013 *)

CROSSREFS

Cf. A004113, A004114, A052316.

Sequence in context: A112699 A093197 A303921 * A185524 A122743 A241031

Adjacent sequences:  A052314 A052315 A052316 * A052318 A052319 A052320

KEYWORD

nonn

AUTHOR

Christian G. Bower, Dec 15 1999

STATUS

approved

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Last modified November 13 04:20 EST 2019. Contains 329085 sequences. (Running on oeis4.)