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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
OFFSET
1,2
LINKS
M. P. Develin and S. P. Sullivant, Markov Bases of Binary Graph Models, Annals of Combinatorics 7 (2003) 441-466.
Christiane Poupard, Deux propriétés des arbres binaires ordonnés stricts, Europ. J. Combin., vol. 10, 1989, pp. 369-374.
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
From Klaus K Haverkamp, Jul 02 2023: (Start)
a(n) = (A002105(n+2) - (n+1)*A002105(n+1))/2.
a(n) = A094503(2n+1,n). (End)
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: A140034 A363024 A162715 * A157382 A174979 A157945
KEYWORD
nonn
AUTHOR
Wenjin Woan, Oct 03 2007
EXTENSIONS
More terms from Michel Marcus, Mar 03 2013
STATUS
approved