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A253095
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Moments of 4-step random walk in 4 dimensions.
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3
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1, 4, 22, 148, 1144, 9784, 90346, 885868, 9115276, 97578688, 1079676448, 12285725632, 143204046496, 1704422018992, 20660609113186, 254522834851516, 3180935346538684, 40269426101933392, 515743456513546072, 6675036087017279056, 87221496402779437696, 1149701868292524559744
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OFFSET
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0,2
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LINKS
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MAPLE
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W := proc(n, nu, twok)
option remember;
local k;
k := twok/2 ;
if n = 2 and nu = 1 then
binomial(2*k+2, k+1)/(k+2) ;
else
add( procname(n-1, nu, 2*j)*binomial(k, j)*(k+nu)!*nu!/(k-j+nu)!/(j+nu)!, j=0..k) ;
simplify(%, GAMMA) ;
end if;
end proc:
W(4, 1, n) ;
end proc:
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MATHEMATICA
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W[n_, nu_, twok_] := W[n, nu, twok] = Module[{k}, k = twok/2; If[n == 2 && nu == 1, Binomial[2k+2, k+1]/(k+2), Sum[W[n-1, nu, 2j]*Binomial[k, j]*(k+nu)!*nu!/(k-j+nu)!/(j+nu)!, {j, 0, k}]]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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