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 A253094 Related to residues of poles of moment function for random walks in 6 dimensions. 1

%I

%S 1,-5,6,2,6,18,66,278,1296,6528,34950,196578,1151610,6981102,43570170,

%T 278841438,1823991630,12162884778,82498605594,568140045918,

%U 3966323992074,28032955095198,200355706872054,1446628270673682,10542888272710224,77496225169484448

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

%H Jonathan M. Borwein, Armin Straub and Christophe Vignat, <a href="http://www.carma.newcastle.edu.au/jon/dwalks.pdf">Densities of short uniform random walks, Part II: Higher dimensions</a>, Preprint, 2015.

%F 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

%p A253094 := proc(k)

%p option remember;

%p local nu,kno ;

%p nu := 2;

%p if k = -1 then

%p 0;

%p elif k = 0 then

%p 1;

%p else

%p kno := k-1 ;

%p 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) ;

%p %/(kno+1)/(kno+nu+1) ;

%p end if;

%p end proc:

%p seq(A253094(k),k=0..40) ; # _R. J. Mathar_, Jun 14 2015

%K sign

%O 0,2

%A _N. J. A. Sloane_, Feb 16 2015

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Last modified May 10 16:34 EDT 2021. Contains 343775 sequences. (Running on oeis4.)