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A004313
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a(n) = binomial coefficient C(2n, n-7).
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4
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1, 16, 153, 1140, 7315, 42504, 230230, 1184040, 5852925, 28048800, 131128140, 600805296, 2707475148, 12033222880, 52860229080, 229911617056, 991493848554, 4244421484512, 18053528883775, 76360380541900, 321387366339585, 1346766106565880, 5621728217559090
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OFFSET
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7,2
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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-7)*(n+7)*a(n) + 2*n*(2*n-1)*a(n-1) = 0. - R. J. Mathar, Jan 24 2018
Sum_{n>=7} 1/a(n) = 41*Pi/(9*sqrt(3)) - 24923/3465.
Sum_{n>=7} (-1)^(n+1)/a(n) = 51094*log(phi)/(5*sqrt(5)) - 7616722/3465, where phi is the golden ratio (A001622). (End)
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MATHEMATICA
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Table[Binomial[2n, n-7], {n, 7, 30}] (* Harvey P. Dale, Nov 27 2013 *)
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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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