A253093 Related to residues of poles of moment function for random walks in 4 dimensions.

1, -2, -2, -6, -24, -114, -606, -3486, -21258, -135582, -896046, -6095490, -42470280, -301938390, -2183873490, -16032229362, -119232361656, -896918310126, -6815685210078, -52262898201642, -404022890110872, -3146342571901278, -24666061437979938, -194550540203413314

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Jonathan M. Borwein, Armin Straub and Christophe Vignat, Densities of short uniform random walks, Part II: Higher dimensions, Preprint, 2015.

Formula

n*(n+1)*a(n) +2*(-5*n^2+10*n-3)*a(n-1) +9*(n-2)*(n-3)*a(n-2)=0. - R. J. Mathar, Jun 14 2015

Maple

A253093 := proc(k)
    option remember;
    local nu, kno ;
    nu := 1;
    if k = -1 then
        0;
    elif k = 0 then
        1;
    else
        kno := k-1 ;
        procname(kno)/2*(20*(kno+1/2)^2-20*(kno+1/2)*nu-4*nu^2+1)-9*(kno-nu)*(kno-2*nu)*procname(kno-1) ;
        %/(kno+1)/(kno+nu+1) ;
    end if;
end proc:
seq(A253093(k), k=0..40) ; # R. J. Mathar, Jun 14 2015
ogf := (x-1)^2*hypergeom([1/3, 4/3], [2], -27*x*(x-1)^2/(9*x-1)^2)/(1-9*x)^(2/3);
series(ogf, x=0, 30); # Mark van Hoeij, Nov 12 2023

Mathematica

a[n_] := a[n] = Switch[n, 0, 1, 1, -2, _, (-9*n^2*a[n-2] + 10*n^2*a[n-1] + 45*n*a[n-2] - 20 n*a[n-1] - 54 a[n-2] + 6 a[n-1])/(n(n+1))];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Apr 15 2023 *)

Crossrefs

Sequence in context: A093453 A301381 A342282 * A052660 A374399 A135407

Adjacent sequences: A253090 A253091 A253092 * A253094 A253095 A253096

Keyword

sign

Author

N. J. A. Sloane, Feb 16 2015

Status

approved