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A073155 Leftmost column sequence of triangle A073153. 4
1, 1, 4, 14, 56, 237, 1046, 4762, 22198, 105430, 508384, 2482297, 12248416, 60980875, 305955356, 1545397464, 7852100294, 40105277640, 205798130604, 1060467961508, 5485199090812, 28469067353686, 148220323891460 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..22.

N. S. S. Gu, N. Y. Li and T. Mansour, 2-Binary trees: bijections and related issues, Discr. Math., 308 (2008), 1209-1221.

FORMULA

Convolution of sequence formed from sum of adjacent terms yields the original sequence without the first term:

a(n+1) = Sum_{k=0..n} [a(k) + a(k-1)] * [a(n-k) + a(n-k-1)], where a(-1)=0.

G.f.: 1/2*(1-(1-4*x*(1+x)^2)^(1/2))/x/(1+x)^2. - Vladeta Jovovic, Oct 10 2003

a(n) = Sum_{k=0..n} C(2k,n-k)*C(k). - Paul Barry, Jul 09 2006

Conjecture: (n+1)*a(n) + (-3*n+4)*a(n-1) + 2*(-6*n+7)*a(n-2) + 2*(-6*n+11)*a(n-3) + 2*(-2*n+5)*a(n-4)=0. - R. J. Mathar, Nov 26 2012

G.f. A(x) satisfies: A(x) = 1 + x * ((1 + x) * A(x))^2. - Ilya Gutkovskiy, Jul 10 2020

EXAMPLE

a(3)=a(0)*[a(2)+a(1)]+[a(1)+a(0)]*[a(1)+a(0)]+[a(2)+a(1)]*a(0) =1*[4+1] + [1+1]*[1+1] + [4+1]*1 = 5 + 2*2 + 5 = 14.

CROSSREFS

Cf. A073153, A073156, A073157.

Sequence in context: A132837 A259808 A149491 * A006212 A126701 A309514

Adjacent sequences:  A073152 A073153 A073154 * A073156 A073157 A073158

KEYWORD

easy,nonn,changed

AUTHOR

Paul D. Hanna, Jul 29 2002

EXTENSIONS

More terms from Vladeta Jovovic, Oct 10 2003

STATUS

approved

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Last modified July 13 10:38 EDT 2020. Contains 335687 sequences. (Running on oeis4.)