OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Jonathan M. Borwein, Armin Straub, James Wan, and Wadim Zudilin, Densities of Short Uniform Random Walks p. 971, Canad. J. Math. 64(2012), 961-990.
FORMULA
p_4(x) = (2*sqrt(16-x^2)*Re(3F2(1/2, 1/2, 1/2; 5/6, 7/6; (16-x^2)^3/(108*x^4))))/(Pi^2*x) where 3F2 is the hypergeometric function.
p_4(2) = (2^(7/3)*Pi)/(3*sqrt(3)*gamma(2/3)^6).
p_4(2) = (2*sqrt(3)*gamma(7/6))/(Pi*gamma(2/3)^2*gamma(5/6)).
EXAMPLE
0.4942337098873326691781895446664234295749970337337829203516164970635637543...
MATHEMATICA
RealDigits[2^(7/3)*Pi/(3*Sqrt[3]*Gamma[2/3]^6), 10, 105] // First
PROG
(PARI) (2^(7/3)*Pi)/(3*sqrt(3)*gamma(2/3)^6) \\ Michel Marcus, Jun 17 2015
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jul 09 2014
STATUS
approved