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A140226
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Binomial transform of [1, 3, 3, 1, 1, -1, 1, -1, 1, ...].
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1
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1, 4, 10, 20, 36, 60, 94, 140, 200, 276, 370, 484, 620, 780, 966, 1180, 1424, 1700, 2010, 2356, 2740, 3164, 3630, 4140, 4696, 5300, 5954, 6660, 7420, 8236, 9110, 10044, 11040, 12100, 13226, 14420
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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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A007318 * [1, 3, 3, 1, 1, -1, 1, -1, 1, ...].
a(n) = n*(11 + n^2)/3 for n >= 1.
G.f.: (1+x^4)/(1-x)^4. (End)
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EXAMPLE
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a(5) = 36 = (1, 4, 6, 4, 1) dot (1, 3, 3, 1, 1) = (1 + 12 + 18 + 4 + 1).
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MAPLE
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MATHEMATICA
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CoefficientList[Series[(1+x^4)/(1-x)^4, {x, 0, 50}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 4, 10, 20, 36}, 50] (* Harvey P. Dale, Aug 17 2021 *)
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PROG
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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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EXTENSIONS
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STATUS
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approved
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