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A360185
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a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*n-4*k,n-2*k).
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5
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1, 2, 5, 18, 65, 234, 859, 3198, 12011, 45422, 172745, 660010, 2531411, 9740590, 37585189, 145376930, 563495201, 2188229290, 8511640099, 33157034510, 129334888721, 505100839930, 1974764074999, 7728329887670, 30272839608101, 118682276550082, 465645693340003
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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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G.f.: 1 / ( sqrt(1-4*x) * (1 + x^2) ).
D-finite with recurrence n*a(n) +2*(-2*n+1)*a(n-1) +n*a(n-2) +2*(-2*n+1)*a(n-3)=0. - R. J. Mathar, Mar 12 2023
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MAPLE
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add((-1)^k*binomial(2*n-4*k, n-2*k), k=0..n/2) ;
end proc:
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PROG
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(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(2*n-4*k, n-2*k));
(PARI) my(N=30, x='x+O('x^N)); Vec(1/(sqrt(1-4*x)*(1+x^2)))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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