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A102893 Number of noncrossing trees with n edges and having degree of the root at least 2. 8
1, 0, 1, 5, 25, 130, 700, 3876, 21945, 126500, 740025, 4382625, 26225628, 158331880, 963250600, 5899491640, 36345082425, 225082957512, 1400431689475, 8749779798375, 54874635255825, 345329274848250, 2179969531405680 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

[a(n+2)]= [1,5,25,130,700,...] is the self-convolution 5th power of A001764. - Philippe Deléham, Nov 11 2009

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200

David Bevan, R Brignall, AE Price, J Pantone, New bounds on the growth rate of 1324-avoiders, arXiv preprint arXiv:1711.10325, 2017

Emanuele Munarini, Shifting Property for Riordan, Sheffer and Connection Constants Matrices, Journal of Integer Sequences, Vol. 20 (2017), Article 17.8.2.

M. Noy, Enumeration of noncrossing trees on a circle, Discrete Math., 180, 301-313, 1998.

FORMULA

a(0)=1; a(n) = 5*binomial(3n-1, n-2)/(3n-1) if n > 0.

G.f.: g - z*g^2, where g = 1 + z*g^3 is the g.f. of the ternary numbers (A001764).

a(n) = A001764(n) - A006013(n-1).

2*n*(2*n+1)*(n-2)*a(n) -3*(n-1)*(3*n-4)*(3*n-2)*a(n-1)=0. - R. J. Mathar, Feb 16 2018

EXAMPLE

a(2)=1 because among the noncrossing trees with 2 edges, namely /_, _\ and /\, only the last one has root degree >1.

MAPLE

a:=proc(n) if n=0 then 1 else 5*binomial(3*n-1, n-2)/(3*n-1) fi end: seq(a(n), n=0..25);

MATHEMATICA

a[0] = 1; a[n_] := 5*Binomial[3n-1, n-2]/(3n-1); Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Mar 01 2018 *)

PROG

(PARI) a(n) = if(n<=1, n==0, 5*binomial(3*n-1, n-2)/(3*n-1)); \\ Andrew Howroyd, Nov 17 2017

CROSSREFS

Column k=0 of A102892 and column k=0 of A102593.

Cf. A001764, A006013.

Sequence in context: A002002 A182626 A184139 * A094602 A207834 A225963

Adjacent sequences:  A102890 A102891 A102892 * A102894 A102895 A102896

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Jan 16 2005

STATUS

approved

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Last modified November 20 06:06 EST 2018. Contains 317385 sequences. (Running on oeis4.)