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A306940
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Expansion of 1/((1 - x)^6 + x^6).
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2
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1, 6, 21, 56, 126, 252, 461, 780, 1209, 1638, 1638, 0, -6187, -23238, -63783, -151316, -326382, -652764, -1217483, -2107560, -3322995, -4538430, -4538430, 0, 16942381, 63239286, 172791861, 408855776, 880983606, 1761967212, 3287837741, 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+5,6*k+5).
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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CoefficientList[Series[1/((1 - x)^6 + x^6), {x, 0, 31}], x] (* Amiram Eldar, May 25 2021 *)
LinearRecurrence[{6, -15, 20, -15, 6, -2}, {1, 6, 21, 56, 126, 252}, 40] (* Harvey P. Dale, May 31 2021 *)
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PROG
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(PARI) {a(n) = sum(k=0, n\6, (-1)^k*binomial(n+5, 6*k+5))}
(PARI) N=66; x='x+O('x^N); Vec(1/((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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