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A253095 Moments of 4-step random walk in 4 dimensions. 1
1, 4, 22, 148, 1144, 9784, 90346, 885868, 9115276, 97578688, 1079676448, 12285725632, 143204046496, 1704422018992, 20660609113186, 254522834851516, 3180935346538684, 40269426101933392, 515743456513546072, 6675036087017279056, 87221496402779437696, 1149701868292524559744 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

J. M. Borwein, A short walk can be beautiful, 2015.

J. M. Borwein, Adventures with the OEIS: Five sequences Tony may like, Guttman 70th [Birthday] Meeting, 2015, revised May 2016.

J. M. Borwein, Adventures with the OEIS: Five sequences Tony may like, Guttman 70th [Birthday] Meeting, 2015, revised May 2016. [Cached copy, with permission]

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:

A253095 := proc(n)

    W(4, 1, n) ;

end proc:

seq(A253095(2*n), n=0..25) ; # R. J. Mathar, Jun 14 2015

CROSSREFS

Sequence in context: A005039 A199418 A112898 * A111529 A228883 A307439

Adjacent sequences:  A253092 A253093 A253094 * A253096 A253097 A253098

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 16 2015

STATUS

approved

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Last modified October 20 10:18 EDT 2019. Contains 328257 sequences. (Running on oeis4.)