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A027819
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a(n) = 7*(n+1)*binomial(n+6,7)/2.
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1
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7, 84, 504, 2100, 6930, 19404, 48048, 108108, 225225, 440440, 816816, 1447992, 2469012, 4069800, 6511680, 10147368, 15444891, 23015916, 33649000, 48348300, 68378310, 95315220, 131105520, 178132500, 239291325, 318073392, 418660704, 546031024, 706074600, 905723280
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OFFSET
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1,1
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COMMENTS
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Number of 14-subsequences of [ 1, n ] with just 6 contiguous pairs.
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LINKS
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FORMULA
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G.f.: 7*(1+3*x)*x/(1-x)^9.
Sum_{n>=1} 1/a(n) = 5969/300 - 2*Pi^2.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2 - 384*log(2)/5 + 13049/300. (End)
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MATHEMATICA
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Table[7*(n + 1)*Binomial[n + 6, 7]/2, {n, 1, 50}] (* Amiram Eldar, Feb 03 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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