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 A030056 a(n) = binomial(2*n+1, n-6). 4
 1, 15, 136, 969, 5985, 33649, 177100, 888030, 4292145, 20160075, 92561040, 417225900, 1852482996, 8122425444, 35240152720, 151532656696, 646626422970, 2741188875414, 11554258485616, 48459472266975 (list; graph; refs; listen; history; text; internal format)
 OFFSET 6,2 LINKS Chai Wah Wu, Table of n, a(n) for n = 6..500 Milan Janjic, Two Enumerative Functions. FORMULA a(n+1) = a(n)*(2*n+2)*(2*n+3)/((n-5)*(n+8)). - Chai Wah Wu, Jan 26 2016 From Amiram Eldar, Jan 24 2022: (Start) Sum_{n>=6} 1/a(n) = 40*Pi/(9*sqrt(3)) - 96827/13860. Sum_{n>=6} (-1)^n/a(n) = 29248*log(phi)/(5*sqrt(5)) - 3486955/2772, where phi is the golden ratio (A001622). (End) MATHEMATICA Table[Binomial[2*n + 1, n - 6], {n, 6, 25}] (* Amiram Eldar, Jan 24 2022 *) PROG (Python) from __future__ import division A030056_list, b = [], 1 for n in range(6, 501): A030056_list.append(b) b = b*(2*n+2)*(2*n+3)//((n-5)*(n+8)) # Chai Wah Wu, Jan 26 2016 CROSSREFS Diagonal 14 of triangle A100257. Cf. A001622. Sequence in context: A155648 A126536 A299033 * A225978 A175707 A123955 Adjacent sequences: A030053 A030054 A030055 * A030057 A030058 A030059 KEYWORD nonn AUTHOR N. J. A. Sloane. STATUS approved

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Last modified March 4 13:15 EST 2024. Contains 370532 sequences. (Running on oeis4.)