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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. 3
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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 06 2002
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)