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A306941
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Expansion of 1/((1 - x)^8 + x^8).
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2
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1, 8, 36, 120, 330, 792, 1716, 3432, 6434, 11424, 19312, 31008, 46512, 62016, 62016, 0, -245156, -961376, -2787760, -7065760, -16478280, -36159840, -75522960, -151045920, -290021896, -534308096, -940325760, -1564496128, -2406819200, -3249142272, -3249142272
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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/8)} (-1)^k*binomial(n+7,8*k+7).
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - 2*a(n-8) for n > 7.
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MATHEMATICA
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CoefficientList[Series[1/((1 - x)^8 + x^8), {x, 0, 30}], x] (* Amiram Eldar, May 25 2021 *)
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PROG
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(PARI) {a(n) = sum(k=0, n\8, (-1)^k*binomial(n+7, 8*k+7))}
(PARI) N=66; x='x+O('x^N); Vec(1/((1-x)^8+x^8))
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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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