A093526 Numerators of even raw moments in the distribution of line lengths for lines picked at random in the unit disk.
1, 1, 5, 7, 42, 22, 429, 715, 4862, 8398, 58786, 52003, 742900, 1337220, 646323, 17678835, 129644790, 79606450, 1767263190, 328206021, 8155422340, 45741281820, 343059613650, 107492012277, 4861946401452, 9183676536076
Offset: 0
Examples
1, 128/(45*Pi), 1, 2048/(525*Pi), 5/3, 16384/(2205*Pi), ...
Links
- Eric Weisstein's World of Mathematics, Disk Line Picking
Programs
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Maple
A195686 := n -> binomial(2*n,n) / igcd(n,binomial(2*n,n)); A093526 := n -> A195686(n+1)/(n+2); # Peter Luschny, Oct 06 2011
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Mathematica
a[n_] := Binomial[2(n+1), n+1]/((n+2) GCD[n+1, Binomial[2(n+1), n+1]]); Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jul 30 2018, after Peter Luschny *) -
PARI
a(n) = denominator((n+1)*(n+2)/binomial(2*n+2, n+1)); \\ Michel Marcus, Jul 30 2018
Formula
a(k) = Numerator[(2*Gamma[3 + n])/((2 + n)*Gamma[2 + n/2]*Gamma[3 + n/2])] for n = 2k.
a(n) = denominator((n+1)/C(n+1)). - Paul Barry, Nov 17 2004
a(n) = A195686(n+1) / (n+2). - Peter Luschny, Oct 06 2011