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A306942
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Expansion of 1/((1 - x)^9 + x^9).
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2
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1, 9, 45, 165, 495, 1287, 3003, 6435, 12870, 24309, 43740, 75411, 124830, 197505, 293436, 389367, 389367, 0, -1562274, -6216183, -18365697, -47600136, -113879520, -257123889, -554298228, -1148646906, -2297293812, -4443424371, -8313049440, -15011769204
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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/9)} (-1)^k*binomial(n+8,9*k+8).
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) for n > 7.
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MATHEMATICA
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CoefficientList[Series[1/((1-x)^9+x^9), {x, 0, 30}], x] (* Harvey P. Dale, Sep 25 2019 *)
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PROG
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(PARI) {a(n) = sum(k=0, n\9, (-1)^k*binomial(n+8, 9*k+8))}
(PARI) N=66; x='x+O('x^N); Vec(1/((1-x)^9+x^9))
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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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