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A225573 Number of trees over all forests of labeled rooted trees in which some (possibly all or none) of the trees have been specially designated. 0
0, 2, 12, 90, 864, 10290, 147456, 2480058, 48000000, 1052307234, 25798901760, 699896958618, 20826335158272, 674680957031250, 23643898043695104, 891412022961534330, 35982083287879778304, 1548474957047229426498, 70778880000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The expected number of trees in each such forest a(n)/A089140(offset) approaches 3 as n gets large.

LINKS

Table of n, a(n) for n=0..18.

FORMULA

a(n) = Sum_{k=0..n} binomial(n-1,k-1)*n^(n-k)*2^k*k = 6*n*(n+2)^(n-2).

MATHEMATICA

nn = 18; tx = Sum[n^(n - 1) x^n/n!, {n, 1, nn}]; Range[0, nn]! CoefficientList[Series[D[Exp[y tx]^2, y] /. y -> 1, {x, 0, nn}], x]

CROSSREFS

Cf. A225497.

Sequence in context: A098926 A074610 A250130 * A155639 A103882 A304979

Adjacent sequences:  A225570 A225571 A225572 * A225574 A225575 A225576

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, May 10 2013

STATUS

approved

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Last modified November 13 07:13 EST 2019. Contains 329085 sequences. (Running on oeis4.)