A253096 Moments of 5-step random walk in 4 dimensions.
1, 5, 35, 305, 3105, 35505, 444225, 5970725, 85068365, 1272022745, 19810304695, 319422093325, 5307057746125, 90508769121165, 1579462112057595, 28130401719357645, 510199561574590125, 9405815167297415025, 175977472926360962295, 3336795660732459377085, 64047222901288457886285
Offset: 0
Keywords
Links
- J. M. Borwein, A short walk can be beautiful, 2015.
- Jonathan M. Borwein, Armin Straub and Christophe Vignat, Densities of short uniform random walks, Part II: Higher dimensions, Preprint, 2015.
Programs
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Maple
W := proc(n,nu,twok) option remember; local k; k := twok/2 ; if n = 2 and nu = 1 then binomial(2*k+2,k+1)/(k+2) ; else add( procname(n-1,nu,2*j)*binomial(k,j)*(k+nu)!*nu!/(k-j+nu)!/(j+nu)!,j=0..k) ; simplify(%,GAMMA) ; end if; end proc: A253096 := proc(n) W(5,1,n) ; end proc: seq(A253096(2*n),n=0..25) ; # R. J. Mathar, Jun 14 2015
Extensions
a(20) corrected by Georg Fischer, May 30 2022