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A340003 Random walk in R^3: Denominators of the expected distance after n steps. 2
1, 1, 3, 8, 15, 576, 105, 46080, 567, 5160960, 99792, 5573836800, 4633200, 163499212800, 277992000, 476109707673600, 231567336000, 2056793937149952000, 281585880576000, 4195859631785902080000, 14514472207872000, 637770664031457116160000, 6676657215621120000 (list; graph; refs; listen; history; text; internal format)
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 denominators.

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.

LINKS

Ludovic Schwob, Table of n, a(n) for n = 0..59

FORMULA

A340002(n)/a(n) ~ 2*sqrt(2*n)/sqrt(3*Pi).

CROSSREFS

See A340002 for numerators.

Sequence in context: A120341 A325904 A094357 * A136532 A030417 A275239

Adjacent sequences:  A340000 A340001 A340002 * A340004 A340005 A340006

KEYWORD

nonn,frac

AUTHOR

Ludovic Schwob, Dec 26 2020

STATUS

approved

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Last modified September 20 10:51 EDT 2021. Contains 347584 sequences. (Running on oeis4.)