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A027812
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a(n) = 7*(n+1)*binomial(n+5,7).
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1
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21, 224, 1260, 5040, 16170, 44352, 108108, 240240, 495495, 960960, 1769768, 3118752, 5290740, 8682240, 13837320, 21488544, 32605881, 48454560, 70662900, 101301200, 142972830, 198918720, 273136500, 370515600, 496989675, 659707776, 867225744, 1129719360, 1459220840
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OFFSET
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2,1
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COMMENTS
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Number of 13-subsequences of [ 1, n ] with just 5 contiguous pairs.
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LINKS
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FORMULA
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G.f.: 7*(3+5x)*x^2/(1-x)^9.
Sum_{n>=2} 1/a(n) = 5*Pi^2/2 - 5909/240.
Sum_{n>=2} (-1)^n/a(n) = 5*Pi^2/4 - 32*log(2) + 791/80. (End)
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MATHEMATICA
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Table[7 * (n+1) * Binomial[n+5, 7], {n, 2, 50}] (* Amiram Eldar, Feb 04 2022 *)
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {21, 224, 1260, 5040, 16170, 44352, 108108, 240240, 495495}, 30] (* Harvey P. Dale, Aug 01 2022 *)
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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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