OFFSET
0,2
LINKS
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
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Feb 16 2015
STATUS
approved