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%I #31 Nov 12 2023 12:08:27
%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="https://arminstraub.com/pub/dwalks">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
%p ogf := (x-1)^4*hypergeom([1/3, 7/3],[3],-27*x*(x-1)^2/(9*x-1)^2)/(1-9*x)^(2/3);
%p series(ogf, x=0, 40); # _Mark van Hoeij_, Nov 12 2023
%t 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))];
%t Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Apr 15 2023 *)
%K sign
%O 0,2
%A _N. J. A. Sloane_, Feb 16 2015
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