

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
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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..n2}(n3)!n^(n2r)/(n2r)!.


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[n2, n] // Round, {n, 1, 50}] (* JeanFrançois Alcover, Jan 15 2014 *)


CROSSREFS

Cf. A057500 = binom(n1, 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



