A253094 Related to residues of poles of moment function for random walks in 6 dimensions.

1, -5, 6, 2, 6, 18, 66, 278, 1296, 6528, 34950, 196578, 1151610, 6981102, 43570170, 278841438, 1823991630, 12162884778, 82498605594, 568140045918, 3966323992074, 28032955095198, 200355706872054, 1446628270673682, 10542888272710224, 77496225169484448

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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

Formula

n*(n+2)*a(n) + 5*(-2*n^2+6*n-1)*a(n-1) + 9*(n-3)*(n-5)*a(n-2) = 0. - R. J. Mathar, Jun 14 2015

Maple

A253094 := proc(k)
    option remember;
    local nu, kno ;
    nu := 2;
    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(A253094(k), k=0..40) ; # R. J. Mathar, Jun 14 2015
ogf := (x-1)^4*hypergeom([1/3, 7/3], [3], -27*x*(x-1)^2/(9*x-1)^2)/(1-9*x)^(2/3);
series(ogf, x=0, 40); # Mark van Hoeij, Nov 12 2023

Mathematica

a[n_] := a[n] = Switch[n, 0, 1, 1, -5, _, (-9*n^2*a[n-2] + 10*n^2*a[n-1] + 72n*a[n-2] - 30n*a[n-1] - 135 a[n-2] + 5a[n-1])/(n(n+2))];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Apr 15 2023 *)

Crossrefs

Sequence in context: A091873 A038690 A154801 * A346046 A217015 A107825

Adjacent sequences: A253091 A253092 A253093 * A253095 A253096 A253097

Keyword

sign

Author

N. J. A. Sloane, Feb 16 2015

Status

approved