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A145564
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a(n) = numerator(Sum_{k=0..n} 1/(binomial(2*k,k)*(k+1))).
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2
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1, 5, 47, 949, 33287, 14273, 7694047, 400101469, 1200312247, 20405339951, 4264717637359, 328055232193, 1275150714976991, 1275150721602467, 2125251205342781, 246529139894912671, 129920856734238187217, 2122119257040297503, 22216466502052353380347, 164401852115363364287267
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OFFSET
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0,2
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COMMENTS
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Previous name was: "Numerators of partial sums of a certain series of inverse central binomial coefficients.Numerators of partial sums of a certain series of inverse central binomial coefficients".
The limit of the rational partial sums r(n), defined below, for n->infinity is (4*sqrt(3)- Pi)*Pi/9. This limit is approximately 1.321776442.
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LINKS
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FORMULA
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a(n) = numerator(r(n)) with r(n)=sum(1/(binomial(2*k,k)*(k+1)),k=0..n), rationals in lowest terms.
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EXAMPLE
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Rationals r(n) (in lowest terms): [1, 5/4, 47/36, 949/720, 33287/25200, 14273/10800, 7694047/5821200,...].
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PROG
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(PARI) a(n) = numerator(sum(k=0, n, 1/(binomial(2*k, k)*(k+1)))); \\ Michel Marcus, Nov 08 2015
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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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EXTENSIONS
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STATUS
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approved
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