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A131638 Increasing binary trees having exactly two vertices with outdegree 1. 0
1, 11, 180, 4288, 141584, 6213288, 350400832, 24718075136, 2133652515072, 221311262045440, 27166907582280704, 3895974311462313984, 645512064907811491840, 122381396964887716078592, 26325690425815766552887296, 6377608610246241663568248832 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

M. P. Develin and S. P. Sullivant, Markov Bases of Binary Graph Models, Annals of Combinatorics 7 (2003) 441-466.

C. Poupard, Deux proprietes des arbres binaires ordonnes stricts, European J. Combin., 10 (1989), 369-374.

LINKS

Table of n, a(n) for n=1..16.

FORMULA

E.g.f. = (3*sec(x/sqrt(2))^2*tan(x/sqrt(2))^2-x*sec(x/sqrt(2))^2*tan(x/sqrt(2))/(sqrt(2)))/2. - Michel Marcus, Mar 03 2013

a(n) ~ (2*n)! * 2^(n+6)*n^3/Pi^(2*n+4). - Vaclav Kotesovec, Sep 25 2013

MATHEMATICA

Table[n!*SeriesCoefficient[1/2*(-((x*Sec[x/Sqrt[2]]^2 *Tan[x/Sqrt[2]]) /Sqrt[2]) + 3*Sec[x/Sqrt[2]]^2 *Tan[x/Sqrt[2]]^2), {x, 0, n}], {n, 2, 40, 2}] (* Vaclav Kotesovec after Michel Marcus, Sep 25 2013 *)

PROG

(PARI) lista(m) = { default(realprecision, 30); x = y + O(y^m); egf = (3*tan(x/sqrt(2))^2/cos(x/sqrt(2))^2-x*tan(x/sqrt(2))/(sqrt(2)*cos(x/sqrt(2))^2))/2; forstep (n=2, m, 2, print1(round(n!*polcoeff(egf, n, y)), ", ")); }  \\ Michel Marcus, Mar 03 2013

CROSSREFS

Sequence in context: A101791 A140034 A162715 * A157382 A174979 A157945

Adjacent sequences:  A131635 A131636 A131637 * A131639 A131640 A131641

KEYWORD

nonn

AUTHOR

Wenjin Woan, Oct 03 2007

EXTENSIONS

More terms from Michel Marcus, Mar 03 2013

STATUS

approved

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Last modified November 12 09:01 EST 2019. Contains 329052 sequences. (Running on oeis4.)