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A093526 Numerators of even raw moments in the distribution of line lengths for lines picked at random in the unit disk. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Disk Line Picking
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
EXAMPLE
1, 128/(45*Pi), 1, 2048/(525*Pi), 5/3, 16384/(2205*Pi), ...
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
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 *)
PROG
(PARI) a(n) = denominator((n+1)*(n+2)/binomial(2*n+2, n+1)); \\ Michel Marcus, Jul 30 2018
CROSSREFS
Sequence in context: A120298 A178342 A117751 * A098512 A234040 A292010
KEYWORD
nonn,frac
AUTHOR
Eric W. Weisstein, Mar 30 2004
STATUS
approved

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Last modified March 19 01:34 EDT 2024. Contains 370952 sequences. (Running on oeis4.)