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A027778
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a(n) = 5*(n+1)*binomial(n+2, 5)/2.
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2
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10, 75, 315, 980, 2520, 5670, 11550, 21780, 38610, 65065, 105105, 163800, 247520, 364140, 523260, 736440, 1017450, 1382535, 1850695, 2443980, 3187800, 4111250, 5247450, 6633900, 8312850, 10331685, 12743325, 15606640, 18986880, 22956120, 27593720, 32986800, 39230730
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OFFSET
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3,1
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COMMENTS
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Number of 8-subsequences of [ 1, n ] with just 2 contiguous pairs.
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LINKS
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FORMULA
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G.f.: 5*x^3*(2+x)/(1-x)^7.
Sum_{n>=3} 1/a(n) = 239/18 - 4*Pi^2/3.
Sum_{n>=3} (-1)^(n+1)/a(n) = 2*Pi^2/3 + 64*log(2)/3 - 383/18. (End)
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MATHEMATICA
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DeleteCases[CoefficientList[Series[5 x^3*(2 + x)/(1 - x)^7, {x, 0, 24}], x], 0] (* Michael De Vlieger, Jul 16 2021 *)
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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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STATUS
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approved
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