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 A004117 Numerators of expansion of (1-x)^(-1/3). 4
 1, 1, 2, 14, 35, 91, 728, 1976, 5434, 135850, 380380, 1071980, 9111830, 25933670, 74096200, 637227320, 1832028545, 5280552865, 137294374490, 397431084050, 1152550143745, 10043651252635, 29217894553120, 85112997176480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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] LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 FORMULA (1/n!) * prod(k=0, n-1, 3k+1) * 3^A054861(n). - Ralf Stephan, Mar 13 2004 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 MATHEMATICA Table[Numerator[Binomial[-1/3, n] (-1)^n], {n, 0, 40}] (* Vincenzo Librandi, Jun 13 2012 *) PROG (PARI) a(n)=prod(k=1, n, 3*k-2)/n!*3^sum(k=1, n, valuation(k, 3)) CROSSREFS Cf. A004128. Cf. A004987, A007559, A047657, A054861, A034689, A053101, A072888. Sequence in context: A145910 A128126 A134647 * A135706 A091520 A218546 Adjacent sequences:  A004114 A004115 A004116 * A004118 A004119 A004120 KEYWORD nonn AUTHOR EXTENSIONS Fixed typo in formula. - Pontus von BrÃ¶mssen, Nov 25 2008 STATUS approved

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Last modified January 17 18:28 EST 2018. Contains 297829 sequences.