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A004315
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a(n) = binomial coefficient C(2n, n-9).
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3
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1, 20, 231, 2024, 14950, 98280, 593775, 3365856, 18156204, 94143280, 472733756, 2311801440, 11058116888, 51915526432, 239877544005, 1093260079344, 4923689695575, 21945588357420, 96926348578605, 424655979547800, 1847253511032930, 7984465725343800, 34315056105966195
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OFFSET
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9,2
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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FORMULA
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-(n-9)*(n+9)*a(n) + 2*n*(2*n-1)*a(n-1) = 0. - R. J. Mathar, Dec 10 2013
Sum_{n>=9} 1/a(n) = 2*Pi/(9*sqrt(3)) + 7457/11440.
Sum_{n>=9} (-1)^(n+1)/a(n) = 453564*log(phi)/(5*sqrt(5)) - 14069064271/720720, where phi is the golden ratio (A001622). (End)
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MATHEMATICA
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Table[Binomial[2*n, n-9], {n, 9, 30}] (* Amiram Eldar, Aug 27 2022 *)
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PROG
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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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