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A307089
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Expansion of (1 - x)^4/((1 - x)^6 + x^6).
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3
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1, 2, 3, 4, 5, 6, 6, 0, -27, -110, -319, -780, -1702, -3404, -6315, -10864, -17051, -23238, -23238, 0, 87021, 325358, 890077, 2107560, 4542526, 9085052, 16950573, 29354524, 46296905, 63239286, 63239286, 0, -236031147, -880918070, -2406788599, -5694626340
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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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a(n) = Sum_{k=0..floor(n/6)} (-1)^k*binomial(n+1,6*k+1).
a(n) = Sum_{i=0..n} Sum_{j=0..n-i} (-1)^j * binomial(i,3*j) * binomial(n-i,3*j).
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - 2*a(n-6) for n > 5.
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MATHEMATICA
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a[n_] := Sum[(-1)^k * Binomial[n+1, 6*k+1], {k, 0, Floor[n/6]}]; Array[a, 36, 0] (* Amiram Eldar, May 14 2021 *)
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PROG
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(PARI) {a(n) = sum(k=0, n\6, (-1)^k*binomial(n+1, 6*k+1))}
(PARI) N=66; x='x+O('x^N); Vec((1-x)^4/((1-x)^6+x^6))
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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