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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.)