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A027801
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a(n) = 5*(n+1)*binomial(n+4,5)/2.
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3
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5, 45, 210, 700, 1890, 4410, 9240, 17820, 32175, 55055, 90090, 141960, 216580, 321300, 465120, 658920, 915705, 1250865, 1682450, 2231460, 2922150, 3782350, 4843800, 6142500, 7719075, 9619155, 11893770, 14599760, 17800200, 21564840, 25970560, 31101840, 37051245
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OFFSET
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1,1
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COMMENTS
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Number of 10-subsequences of [ 1, n ] with just 4 contiguous pairs.
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LINKS
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FORMULA
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G.f.: 5*(1+2x)*x/(1-x)^7.
Sum_{n>=1} 1/a(n) = 241/18 - 4*Pi^2/3.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*Pi^2/3 - 64*log(2)/3 + 151/18. (End)
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MATHEMATICA
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Table[5(n+1) Binomial[n+4, 5]/2, {n, 30}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {5, 45, 210, 700, 1890, 4410, 9240}, 30] (* Harvey P. Dale, Dec 13 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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STATUS
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approved
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