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A291532 Number of trees in all forests of (unlabeled) rooted identity trees with n vertices. 3
0, 1, 1, 3, 4, 9, 19, 40, 84, 186, 413, 922, 2082, 4733, 10831, 24928, 57648, 133923, 312393, 731328, 1717784, 4047111, 9561517, 22647521, 53770164, 127941813, 305046676, 728688803, 1743752229, 4179697971, 10034077377, 24123567285, 58076419495, 139996849639 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = Sum_{k>=1} k * A227774(n+1,k).

a(n) = Sum_{h=0..n} Sum_{t=0..n-h} t * A291529(n,h,t).

EXAMPLE

a(4) = 4:

:   o   :   o  o   :     o     :

:   |   :   |      :    / \    :

:   o   :   o      :   o   o   :

:   |   :   |      :   |       :

:   o   :   o      :   o       :

:   |   :          :           :

:   o   :          :           :

:       :          :           :

MAPLE

b:= proc(n, i, t) option remember; expand(`if`(n=0 or i=1,

       `if`(n<2, x^(t*n), 0), b(n, i-1, t)+add(binomial(

       b(i-1$2, 0), j)*x^(t*j)*b(n-i*j, i-1, t), j=1..n/i)))

    end:

a:= n-> (p-> add(i*coeff(p, x, i), i=1..degree(p)))(b(n$2, 1)):

seq(a(n), n=0..35);

CROSSREFS

Cf. A004111, A005197, A227774, A291529.

Sequence in context: A028344 A219680 A078010 * A110810 A247579 A282615

Adjacent sequences:  A291529 A291530 A291531 * A291533 A291534 A291535

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 25 2017

STATUS

approved

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Last modified August 13 02:09 EDT 2020. Contains 336441 sequences. (Running on oeis4.)