A225573 - OEIS

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, 2, 12, 90, 864, 10290, 147456, 2480058, 48000000, 1052307234, 25798901760, 699896958618, 20826335158272, 674680957031250, 23643898043695104, 891412022961534330, 35982083287879778304, 1548474957047229426498, 70778880000000000000000

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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: A074610 A372109 A250130 * A354233 A155639 A333473

Adjacent sequences: A225570 A225571 A225572 * A225574 A225575 A225576

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, May 10 2013

STATUS

approved