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 A227917 Number of semi-increasing binary plane trees with n vertices. 1
 1, 4, 26, 232, 2624, 35888, 575280, 10569984, 218911872, 5044346112, 127980834816, 3544627393536, 106408500206592, 3441351475359744, 119279906031888384, 4410902376303722496, 173335758665503997952, 7213199863532804702208, 316878056718379090771968 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the number of semi-increasing plane binary trees with n vertices, which are labeled binary plane trees where each vertex with two children has a label less than the label of each of its descendants. LINKS Brad R. Jones, Table of n, a(n) for n = 1..100 B. R. Jones, On tree hook length formulas, Feynman rules and B-series, Master's thesis, Simon Fraser University, 2014. FORMULA E.g.f: 2/(2+log(1-2*x))-1. E.g.f. A(x) satisfies the differential equation A'(x) = (1+2*A(x)+A(x)^2)/(1-2*x). a(n) ~ n! * 2^(n+1)*exp(2*n)/(exp(2)-1)^(n+1). - Vaclav Kotesovec, Oct 30 2013 EXAMPLE Examples of some semi-increasing binary plane trees of 4 vertices:   ----------       1      / \     4   2    /   3   ----------       1      / \     3   2    /   4   ----------       3      /     1    / \   4   2   ----------       3      /     1      \       2        \         4   ----------       1      /     2      \       3      /     4   ---------- The following is NOT a semi-increasing binary tree because vertex 2 has two children and has vertex 1 as a descendant.   ----------       2      / \     3   4    /   1   ---------- MAPLE seq(coeff(taylor(2/(2+log(1-2*z))-1, z, 51), z^i)*i!, i=1..50); MATHEMATICA Rest[CoefficientList[Series[2/(2+Log[1-2*x])-1, {x, 0, 20}], x]*Range[0, 20]!] (* Vaclav Kotesovec, Oct 30 2013 *) CROSSREFS Sequence in context: A293915 A107879 A066224 * A136227 A000310 A054360 Adjacent sequences:  A227914 A227915 A227916 * A227918 A227919 A227920 KEYWORD nonn AUTHOR Brad R. Jones, Oct 22 2013 STATUS approved

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Last modified October 16 03:27 EDT 2019. Contains 328039 sequences. (Running on oeis4.)