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%I #41 Aug 04 2022 06:04:43
%S 1,1,3,8,15,576,105,46080,567,5160960,99792,5573836800,4633200,
%T 163499212800,277992000,476109707673600,231567336000,
%U 2056793937149952000,281585880576000,4195859631785902080000,14514472207872000,637770664031457116160000,6676657215621120000
%N Random walk in R^3: Denominators of the expected distance after n steps.
%C 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 denominators.
%C 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 denominators.
%H Ludovic Schwob, <a href="/A340003/b340003.txt">Table of n, a(n) for n = 0..99</a>
%F A340002(n)/a(n) ~ 2*sqrt(2*n)/sqrt(3*Pi).
%F A340002(n)/a(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
%Y See A340002 for numerators.
%K nonn,frac
%O 0,3
%A _Ludovic Schwob_, Dec 26 2020
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