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A027768
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a(n) = (n+1)*binomial(n+1,8).
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1
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8, 81, 450, 1815, 5940, 16731, 42042, 96525, 205920, 413270, 787644, 1436058, 2519400, 4273290, 7034940, 11277222, 17651304, 27039375, 40619150, 59942025, 87026940, 124472205, 175587750, 244550475, 336585600, 458177148, 617310936, 823753700, 1089372240
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OFFSET
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7,1
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COMMENTS
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Number of 10-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 (10,-45,120,-210,252,-210,120,-45,10,-1).
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FORMULA
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G.f.: (8+x)*x^7/(1-x)^10.
Sum_{n>=7} 1/a(n) = 48877/3675 - 4*Pi^2/3.
Sum_{n>=7} (-1)^(n+1)/a(n) = 2*Pi^2/3 + 38656*log(2)/105 - 2884681/11025. (End)
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MATHEMATICA
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Table[(n+1)Binomial[n+1, 8], {n, 7, 40}] (* Harvey P. Dale, Jul 08 2017 *)
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PROG
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(PARI) a(n) = (n+1)*binomial(n+1, 8); \\ Michel Marcus, Jan 31 2014
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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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