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A071736
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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.
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3
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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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FORMULA
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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