|
|
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
|
|
|
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
|
|
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));
|
|
MATHEMATICA
|
a[n_] := Binomial[2(n+1), n+1]/((n+2) GCD[n+1, Binomial[2(n+1), n+1]]);
|
|
PROG
|
(PARI) a(n) = denominator((n+1)*(n+2)/binomial(2*n+2, n+1)); \\ Michel Marcus, Jul 30 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|