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A093527
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Denominators of even raw moments in the distribution of line lengths for lines picked at random in the unit disk.
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7
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1, 1, 3, 2, 5, 1, 7, 4, 9, 5, 11, 3, 13, 7, 1, 8, 17, 3, 19, 1, 7, 11, 23, 2, 25, 13, 27, 1, 29, 15, 31, 16, 11, 17, 5, 9, 37, 19, 39, 2, 41, 1, 43, 11, 1, 23, 47, 4, 49, 25, 17, 13, 53, 9, 55, 7, 19, 29, 59, 5, 61, 31, 21, 32, 13, 1, 67, 17, 23, 7, 71, 2, 73, 37, 5, 19, 1, 13, 79
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..78.
Eric Weisstein's World of Mathematics, Disk Line Picking
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FORMULA
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a(k) = Denominator[(2*Gamma[3 + n])/((2 + n)*Gamma[2 + n/2]*Gamma[3 + n/2])] for n = 2k.
a(n-1)=numerator(n(n+1)/binomial(2n, n)); a(n)=numerator((n+1)(n+2)/binomial(2(n+1), n+1)); a(n)=numerator(binomial(n+2, 2)/(2binomial(2(n+1), n+1))). - Paul Barry, Sep 11 2004
a(n-1)=numerator(n/C(n)); a(n)=numerator((n+1)/C(n+1)) - Paul Barry, Nov 17 2004
a(n)=denominator(binomial(2n, n)/n). - Enrique Pérez Herrero, Oct 05 2011
a(n)=n/gcd(n,binomial(2n,n)). - Peter Luschny, Oct 05 2011
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EXAMPLE
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1, 128/(45*Pi), 1, 2048/(525*Pi), 5/3, 16384/(2205*Pi), ...
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MAPLE
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A093527 := n -> n / igcd(n, binomial(2*n, n)): - Peter Luschny, Oct 05 2011
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MATHEMATICA
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A093527[n_]:=Denominator[Binomial[2n, n]/n]; Array[A093527, 200] (* Enrique Pérez Herrero, Oct 05 2011 *)
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CROSSREFS
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Cf. A093070, A093526, A093528, A093529.
Second column of A098505.
Cf. A000108.
Sequence in context: A129538 A076934 A111701 * A088233 A056008 A074830
Adjacent sequences: A093524 A093525 A093526 * A093528 A093529 A093530
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KEYWORD
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nonn,frac
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AUTHOR
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Eric W. Weisstein, Jan 04, 1970
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STATUS
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approved
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