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A124087 9th column of Catalan triangle A009766. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
15,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = C(n,8)-C(n,6).
a(n) = A214292(n+15,7). - Reinhard Zumkeller, Jul 12 2012
From Amiram Eldar, Sep 06 2022: (Start)
Sum_{n>=15} 1/a(n) = 12515/11594583.
Sum_{n>=15} (-1)^(n+1)/a(n) = 1942528*log(2)/6435 - 60651032147/289864575. (End)
MAPLE
[seq(binomial(n, 8)-binomial(n, 6), n=15..45)];
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A238136 A060364 A243834 * A244105 A264181 A064305
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, Nov 25 2006
STATUS
approved

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Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)