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Search: id:A130545
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| A130545 |
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Numerators of 2*sum(1/binomial(2*k,k),k=1..n), n>=1. |
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+0
2
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| 1, 4, 43, 307, 463, 10201, 24121, 88453, 1503743, 28571327, 680271, 54761843, 156462429, 111170677, 245020174253, 7595625419003, 2531875141141, 17723125990639, 655755661678837, 655755661685297, 867289746102097
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OFFSET
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1,2
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COMMENT
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Denominators are given by A130546.
Partial sums (in lowest terms) for a series of (2/27)*(9+2*Pi*sqrt(3)).
The rationals r(n):=2*sum(1/binomial(2*k,k),k=1..n) tend, in the limit n->infinity, to(2/27)*(9+2*Pi*sqrt(3)), which is approximately 1.472799718.
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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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W. Lang, Rationals and limit.
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FORMULA
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a(n)=numer(r(n)), n>=1, with the rationals defined above.
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EXAMPLE
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Rationals r(n): [1, 4/3, 43/30, 307/210, 463/315, 10201/6930, 24121/16380,...].
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CROSSREFS
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Cf. A130547/A130548 for s(n):=r(n)-2/3.
Adjacent sequences: A130542 A130543 A130544 this_sequence A130546 A130547 A130548
Sequence in context: A140055 A134356 A111829 this_sequence A027311 A074702 A015084
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jul 13 2007
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