OFFSET
0,3
COMMENTS
The random variables X_n are defined by X_0 = 0 and X_(n+1) = X_n + U_n where U_n are i.i.d. random variables with uniform distribution on the 2-dimensional sphere. Then a(n) = E(|X_n|), take numerators.
Let (V_n)_n be i.i.d. random variables with uniform distribution on the interval [-2,2]. Then a(n) = E(|V_1+...+V_n|), take numerators.
LINKS
Ludovic Schwob, Table of n, a(n) for n = 0..99
FORMULA
a(n)/A340003(n) ~ 2*sqrt(2*n)/sqrt(3*Pi).
a(n)/A340003(n) = (1/(2^(n-2) * (n+1)!)) * Sum_{k=0..floor((n-1)/2)} (-1)^k * C(n,k) * (n-2*k)^(n+1). - Ludovic Schwob, Jun 11 2022
EXAMPLE
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Ludovic Schwob, Dec 26 2020
STATUS
approved