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A253093
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Related to residues of poles of moment function for random walks in 4 dimensions.
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1
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1, -2, -2, -6, -24, -114, -606, -3486, -21258, -135582, -896046, -6095490, -42470280, -301938390, -2183873490, -16032229362, -119232361656, -896918310126, -6815685210078, -52262898201642, -404022890110872, -3146342571901278, -24666061437979938, -194550540203413314
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OFFSET
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0,2
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LINKS
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FORMULA
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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
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MAPLE
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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:
ogf := (x-1)^2*hypergeom([1/3, 4/3], [2], -27*x*(x-1)^2/(9*x-1)^2)/(1-9*x)^(2/3);
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MATHEMATICA
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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))];
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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