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A004117
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Numerators of expansion of (1-x)^(-1/3).
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7
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1, 1, 2, 14, 35, 91, 728, 1976, 5434, 135850, 380380, 1071980, 9111830, 25933670, 74096200, 637227320, 1832028545, 5280552865, 137294374490, 397431084050, 1152550143745, 10043651252635, 29217894553120, 85112997176480
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OFFSET
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0,3
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COMMENTS
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For n >= 1, a(n) is also the numerator of beta(n+1/3,2/3)*sqrt(27)/(2*Pi). - Groux Roland, May 17 2011
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LINKS
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FORMULA
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Numerators in (1-3t)^(-1/3) = 1 + t + 2*t^2 + (14/3)*t^3 + (35/3)*t^4 + (91/3)*t^5 + (728/9)*t^6 + (1976/9)*t^7 + (5434/9)*t^8 + ... = 1 + t + 4*t^2/2! + 28*t^3/3! + 280*t^4/4! + 3640*t^5/5! + 58240*t^6/6! + ... = e.g.f. for triple factorials A007559 (cf. A094638). - Tom Copeland, Dec 04 2013
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MATHEMATICA
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Table[Numerator[Binomial[-1/3, n] (-1)^n], {n, 0, 40}] (* Vincenzo Librandi, Jun 13 2012 *)
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PROG
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(PARI) a(n)=prod(k=1, n, 3*k-2)/n!*3^sum(k=1, n, valuation(k, 3))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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