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A129936
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a(n) = (n-2)*(n+3)*(n+2)/6.
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5
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-2, -2, 0, 5, 14, 28, 48, 75, 110, 154, 208, 273, 350, 440, 544, 663, 798, 950, 1120, 1309, 1518, 1748, 2000, 2275, 2574, 2898, 3248, 3625, 4030, 4464, 4928, 5423, 5950, 6510, 7104, 7733, 8398, 9100, 9840, 10619, 11438, 12298, 13200, 14145, 15134, 16168, 17248
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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a(n) = binomial(n + 3, 3) - (n + 3)*(n + 2)/2.
G.f.: (x^3-4*x^2+6*x-2)/(x-1)^4. - Colin Barker, Sep 05 2012
Sum_{n>=3} 1/a(n) = 77/200.
Sum_{n>=3} (-1)^(n+1)/a(n) = 363/200 - 12*log(2)/5. (End)
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MAPLE
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MATHEMATICA
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f[n_] = Binomial[n + 3, 3] - (n + 3)*(n + 2)/2; Table[f[n], {n, 0, 30}]
LinearRecurrence[{4, -6, 4, -1}, {-2, -2, 0, 5}, 50] (* Harvey P. Dale, Jul 03 2020 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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