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A291559 Total height of all (unlabeled) rooted identity trees with n vertices. 2
0, 0, 1, 2, 5, 10, 23, 52, 120, 275, 644, 1508, 3558, 8418, 20012, 47699, 114082, 273476, 657250, 1582817, 3819514, 9233059, 22356918, 54216429, 131663670, 320158789, 779461271, 1899830067, 4635492672, 11321595218, 27677333555, 67720658475, 165835173692 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

FORMULA

a(n) = Sum_{h=0..n-2} Sum_{t=1..n-1-h} (h+1) * A291529(n-1,h,t).

EXAMPLE

: a(5) = 10 = 4 + 3 + 3 : a(4) = 5 = 3 + 2 :

:                       :                  :

:    o    o      o      :    o    o        :

:    |    |     / \     :    |   / \       :

:    o    o    o   o    :    o  o   o      :

:    |   / \   |        :    |  |          :

:    o  o   o  o        :    o  o          :

:    |  |      |        :    |             :

:    o  o      o        :    o             :

:    |                  :                  :

:    o                  :                  :

:                       :                  :

MAPLE

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

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

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

    end:

g:= (n, h)-> b(n$2, 1, h)-`if`(h=0, 0, b(n$2, 1, h-1)):

F:= (n, h, t)-> coeff(g(n, h), x, t):

a:= n-> add(add((h+1)*F(n-1, h, t), t=1..n-1-h), h=0..n-2):

seq(a(n), n=0..37);

CROSSREFS

Cf. A001853, A004111, A291529.

Sequence in context: A116953 A099516 A293741 * A297074 A099963 A152784

Adjacent sequences:  A291556 A291557 A291558 * A291560 A291561 A291562

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 26 2017

STATUS

approved

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)