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A253096 Moments of 5-step random walk in 4 dimensions. 1
1, 5, 35, 305, 3105, 35505, 444225, 5970725, 85068365, 1272022745, 19810304695, 319422093325, 5307057746125, 90508769121165, 1579462112057595, 28130401719357645, 510199561574590125, 9405815167297415025, 175977472926360962295, 3336795660732459377085, 6404722290128845788628 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..20.

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.

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

CROSSREFS

Sequence in context: A027392 A291813 A177354 * A305964 A226739 A109253

Adjacent sequences:  A253093 A253094 A253095 * A253097 A253098 A253099

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 16 2015

STATUS

approved

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Last modified May 15 22:20 EDT 2021. Contains 343934 sequences. (Running on oeis4.)