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A130547
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Numerators of 6*((Sum_{k=1..n} 1/binomial(2*k,k)) - 1/3), n >= 1.
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3
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1, 2, 23, 167, 253, 5581, 13201, 48413, 823063, 15638407, 1117033, 89921239, 256917887, 60848977, 134111147453, 4157445588203, 1385815197541, 9700706385439, 358926136286437, 358926136292897, 474708760905697
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OFFSET
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1,2
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COMMENTS
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The partial sums (in lowest terms) r(n) = 6*((Sum_{k=1..n} 1/binomial(2*k,k)) - 1/3) tend, for n->infinity, to 4*Pi*sqrt(3)/9, which is approximately 2.418399153.
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 89, Exercise (with a misprint).
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LINKS
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FORMULA
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a(n) = numerator(r(n)), n >= 1, with the rationals defined above.
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MATHEMATICA
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Table[6*(Sum[1/Binomial[2k, k], {k, n}]-1/3), {n, 30}]//Numerator (* Harvey P. Dale, Jul 07 2021 *)
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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STATUS
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approved
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