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A027804
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a(n) = 14*(n+1)*binomial(n+4,8).
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0
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70, 756, 4410, 18480, 62370, 180180, 462462, 1081080, 2342340, 4764760, 9189180, 16930368, 29980860, 51279480, 85058820, 137287920, 216228474, 333125100, 503052550, 745945200, 1087836750, 1562340780, 2212405650, 3092380200, 4270429800, 5831345520, 7879792536
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OFFSET
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4,1
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COMMENTS
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Number of 13-subsequences of [ 1, n ] with just 4 contiguous pairs.
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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.: 14*(5+4x)*x^4/(1-x)^10.
Sum_{n>=4} 1/a(n) = 10*Pi^2/3 - 145013/4410.
Sum_{n>=4} (-1)^n/a(n) = 5*Pi^2/3 + 128*log(2)/7 - 42793/1470. (End)
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MATHEMATICA
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Table[14 * (n+1) * Binomial[n+4, 8], {n, 4, 50}] (* Amiram Eldar, Feb 04 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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