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A071736 Expansion of (1+x^3*C^3)*C^3, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108. 2
1, 3, 9, 29, 96, 324, 1111, 3861, 13572, 48178, 172482, 622098, 2258416, 8246190, 30264435, 111585765, 413126460, 1535267250, 5724840990, 21413721510, 80326153440, 302105210160, 1138957917318, 4303550907234, 16294686579016 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = number of Dyck (n+3)-paths whose initial ascent has length divisible by 3. For example, UUUUDDUDDD has initial ascent of length 4 and a(1) counts UUUDUDDD, UUUDDUDD, UUUDDDUD. - David Callan, Jul 25 2005

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

a(n) ~ 15*4^n/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Mar 21 2014

MATHEMATICA

CoefficientList[Series[(1 + x^3 ((1 - (1 - 4 x)^(1/2))/(2 x))^3) ((1 - (1 - 4 x)^(1/2))/(2 x))^3, {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 21 2014 *)

CROSSREFS

Sequence in context: A289448 A071732 A289804 * A286955 A148938 A082306

Adjacent sequences:  A071733 A071734 A071735 * A071737 A071738 A071739

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 06 2002

STATUS

approved

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Last modified July 15 04:34 EDT 2020. Contains 335763 sequences. (Running on oeis4.)