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

Author

N. J. A. Sloane, Feb 16 2015

Keywords

• nonn

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.

Crossrefs

Cf. A253095 (4-step), A253097 (6-step).

Programs

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