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A056616
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Numerator of binomial(2n,n)/(2n+1).
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4
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1, 2, 6, 20, 70, 252, 924, 1144, 12870, 48620, 184756, 705432, 2704156, 10400600, 40116600, 155117520, 200360130, 466721244, 9075135300, 11781754600, 137846528820, 538257874440, 140273264248, 8233430727600, 32247603683100
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OFFSET
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0,2
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COMMENTS
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The denominators are given in A056617.
It is easy to type binomial(2n,n)/(2n+1) by mistake, when one really wants the Catalan numbers binomial(2n,n)/(n+1), A000108.
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LINKS
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FORMULA
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Numerators of the rationals r(n) = binomial(2n,n)/(2n+1) with G.f.: 1/(2*sqrt(x))*arcsin(2*sqrt(x)). [Vladimir Kruchinin, May 31 2013]
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EXAMPLE
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The rationals r(n) begin: 1, 2/3, 6/5, 20/7, 70/9, 252/11, 924/13, 1144/5, 12870/17, ...
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MAPLE
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seq(numer(binomial(2*n, n)/(2*n+1)), n=0..50); # Robert Israel, Feb 21 2017
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MATHEMATICA
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Numerator[Table[Binomial[2n, n]/(2n+1), {n, 0, 30}]] (* Harvey P. Dale, Jul 25 2013 *)
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PROG
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(PARI) a(n) = numerator(binomial(2*n, n)/(2*n+1)) \\ Felix Fröhlich, Feb 21 2017
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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