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A129137 Number of trees on [n], rooted at 1, in which 2 is a descendant of 3. 5
0, 0, 1, 5, 37, 366, 4553, 68408, 1206405, 24447440, 560041201, 14315792256, 404057805989, 12482986261760, 419042630871225, 15189786100468736, 591374264243364037, 24612549706061862912, 1090556290466098198625 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Washington G. Bomfim, Table of n, a(n) for n = 1..50

H. Bergeron, E. M. F. Curado, J. P. Gazeau and L. M. C. S. Rodrigues, A note about combinatorial sequences and Incomplete Gamma function, arXiv preprint arXiv: 1309.6910, 2013

FORMULA

The following formula counts these trees by the length r of the path from 1 to 3: Sum_{r=1..n-2}(n-3)!n^(n-2-r)/(n-2-r)!.

EXAMPLE

a(4)=5 counts {1->3->2, 1->4}, {1->3->2, 3->4}, {1->3->2->4}, {1->3->4->2}, {1->4->3->2}.

MATHEMATICA

Table[Exp[n]*Gamma[n-2, n] // Round, {n, 1, 50}] (* Jean-Fran├žois Alcover, Jan 15 2014 *)

CROSSREFS

Cf. A057500 = binom(n-1, 2)a(n).

Sequence in context: A025168 A084358 A050351 * A055869 A208231 A112937

Adjacent sequences:  A129134 A129135 A129136 * A129138 A129139 A129140

KEYWORD

nonn

AUTHOR

David Callan, Mar 30 2007

STATUS

approved

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Last modified December 20 20:13 EST 2014. Contains 252289 sequences.