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A124087
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9th column of Catalan triangle A009766.
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2
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1430, 4862, 11934, 25194, 48450, 87210, 149226, 245157, 389367, 600875, 904475, 1332045, 1924065, 2731365, 3817125, 5259150, 7152444, 9612108, 12776588, 16811300, 21912660, 28312548, 36283236, 46142811, 58261125, 73066305, 91051857, 112784399, 138912059
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OFFSET
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15,1
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LINKS
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FORMULA
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a(n) = C(n,8)-C(n,6).
Sum_{n>=15} 1/a(n) = 12515/11594583.
Sum_{n>=15} (-1)^(n+1)/a(n) = 1942528*log(2)/6435 - 60651032147/289864575. (End)
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MAPLE
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[seq(binomial(n, 8)-binomial(n, 6), n=15..45)];
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MATHEMATICA
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CoefficientList[Series[(429*z^7 - 3432*z^6 + 11880*z^5 - 23100*z^4 + 27300*z^3 - 19656*z^2 + 8008*z - 1430)/(z - 1)^9, {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 16 2011 *)
Table[Binomial[n, 8]-Binomial[n, 6], {n, 15, 60}] (* or *) LinearRecurrence[ {9, -36, 84, -126, 126, -84, 36, -9, 1}, {1430, 4862, 11934, 25194, 48450, 87210, 149226, 245157, 389367}, 30] (* Harvey P. Dale, Apr 15 2017 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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