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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, Robert Brignall, Andrew Elvey Price and Jay Pantone, A structural characterisation of Av(1324) and new bounds on its growth rate, arXiv preprint arXiv:1711.10325 [math.CO], 2017-2019. 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 January 21 21:30 EST 2020. Contains 331128 sequences. (Running on oeis4.)