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A027774
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a(n) = (n+1)*binomial(n+1,14).
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2
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14, 225, 1920, 11560, 55080, 220932, 775200, 2441880, 7034940, 18795370, 47070144, 111435000, 251100200, 541574100, 1123264800, 2249204040, 4362680250, 8220658275, 15085939200, 27020703600, 47327171760, 81198579000, 136666699200, 225962211600, 367443055800
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OFFSET
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13,1
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COMMENTS
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Number of 16-subsequences of [ 1, n ] with just 1 contiguous pair.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
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FORMULA
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G.f.: (14+x)*x^13/(1-x)^16.
Sum_{n>=13} 1/a(n) = 107159834863/4637833200 - 7*Pi^2/3.
Sum_{n>=13} (-1)^(n+1)/a(n) = 7*Pi^2/6 + 125673472*log(2)/6435 - 62835162326017/4637833200. (End)
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MATHEMATICA
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Table[(n+1)Binomial[n+1, 14], {n, 13, 40}] (* Harvey P. Dale, Nov 04 2017 *)
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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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