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A154232
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a(2n) = (n^2-n-1) + a(2n-2), a(2n+1) = (n^2-n-1)*a(2n-1), with a(0)=0 and a(1)=1.
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1
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0, 1, -1, -1, 0, -1, 5, -5, 16, -55, 35, -1045, 64, -30305, 105, -1242505, 160, -68337775, 231, -4851982025, 320, -431826400225, 429, -47069077624525, 560, -6166049168812775, 715, -955737621165980125, 896, -172988509431042402625
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OFFSET
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0,7
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COMMENTS
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LINKS
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FORMULA
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a(2*n+1) = cos(Pi*sqrt(5)/2)*Gamma(n+1/2-sqrt(5)/2)*Gamma(n+1/2+sqrt(5)/2)/Pi.
a(2*n+1) = (-1)^n*A130031(n). (End)
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MAPLE
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a[0]:= 0: a[1]:= 1:
for n from 1 to 49 do
a[2*n]:= (n^2-n-1) +a[2*n-2];
a[2*n+1]:= (n^2-n-1)*a[2*n-1];
od:
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MATHEMATICA
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(* First program *)
b[n_]:= b[n]= If[n==0, 0, n^2 -n -1 + b[n-1]];
c[n_]:= c[n]= If[n==0, 1, (n^2 -n -1)*c[n-1]];
Flatten[Table[{b[n], c[n]}, {n, 0, 15}]] (* modified by G. C. Greubel, Mar 02 2021 *)
(* Second program *)
a[n_]:= a[n]= If[n<2, n, If[EvenQ[n], ((n^2-2*n-4)/4) + a[n-2], ((n^2-4*n-1)/4)*a[n-2]]];
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PROG
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(Sage)
def a(n):
if (n<2): return n
elif (n%2==0): return ((n^2-2*n-4)/4) + a(n-2)
else: return ((n^2-4*n-1)/4)*a(n-2)
(Magma)
function a(n)
if n lt 2 then return n;
elif (n mod 2 eq 0) then return ((n^2-2*n-4)/4) + a(n-2);
else return ((n^2-4*n-1)/4)*a(n-2);
end if; return a;
end function;
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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