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 A093527 Denominators of even raw moments in the distribution of line lengths for lines picked at random in the unit disk. 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Eric Weisstein's World of Mathematics, Disk Line Picking FORMULA 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 EXAMPLE 1, 128/(45*Pi), 1, 2048/(525*Pi), 5/3, 16384/(2205*Pi), ... MAPLE A093527 := n -> n / igcd(n, binomial(2*n, n)): # Peter Luschny, Oct 05 2011 MATHEMATICA A093527[n_]:=Denominator[Binomial[2n, n]/n]; Array[A093527, 200] (* Enrique Pérez Herrero, Oct 05 2011 *) CROSSREFS 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 KEYWORD nonn,frac AUTHOR Eric W. Weisstein, Mar 30 2004 STATUS approved

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