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A027771
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a(n) = (n+1)*binomial(n+1,11).
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2
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11, 144, 1014, 5096, 20475, 69888, 210392, 572832, 1436058, 3359200, 7407036, 15519504, 31097794, 59907456, 111435000, 200880160, 352023165, 601277040, 1003321410, 1638819000, 2624841765, 4128783360, 6386711760, 9727323840, 14602906500, 21628990656
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OFFSET
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10,1
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COMMENTS
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Number of 13-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 (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
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FORMULA
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G.f.: (11+x)*x^10/(1-x)^13.
Sum_{n>=10} 1/a(n) = 11*Pi^2/6 - 57138257/3175200.
Sum_{n>=10} (-1)^n/a(n) = 11*Pi^2/12 + 822272*log(2)/315 - 5773608863/3175200. (End)
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MATHEMATICA
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Table[(n+1)*Binomial[n+1, 11], {n, 10, 35}] (* Amiram Eldar, Jan 30 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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