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A117671
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a(n) = binomial(3*n+1, n+1).
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10
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1, 6, 35, 210, 1287, 8008, 50388, 319770, 2042975, 13123110, 84672315, 548354040, 3562467300, 23206929840, 151532656696, 991493848554, 6499270398159, 42671977361650, 280576272201225
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: (2*(-1+Hypergeometric2F1[-(1/3),1/3,-(1/2),(27*x)/4]))/(3*x). - Harvey P. Dale, Jul 19 2011
G.f.: A(x) = B'(x)/B(x)-B'(x)-1/x, where B(x) = 4/3*sin(1/3*asin(sqrt((27*x)/4)))^2. - Vladimir Kruchinin, Nov 26 2014
With an extra initial term equal to 1, the o.g.f. equals f(x)/g(x)^2, where f(x) is the o.g.f. for A005809 and g(x) is the o.g.f. for A001764.
a(n+1) = 3*(3*n+2)*(3*n+4)*a(n)/(2*(n+2)*(2*n+1)). - Robert Israel, Oct 10 2017
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EXAMPLE
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if n=0 then C(3*0+1,0+1) = C(1,1) = 1.
if n=10 then C(3*10+1,10+1) = C(31,11) = 84672315.
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MAPLE
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MATHEMATICA
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Table[Binomial[3n+1, n+1], {n, 0, 20}] (* Harvey P. Dale, Jul 19 2011 *)
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PROG
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(Haskell)
(PARI) vector(30, n, n--; binomial(3*n+1, n+1)) \\ Altug Alkan, Nov 04 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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