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%I #18 Sep 06 2022 02:59:00
%S 1430,4862,11934,25194,48450,87210,149226,245157,389367,600875,904475,
%T 1332045,1924065,2731365,3817125,5259150,7152444,9612108,12776588,
%U 16811300,21912660,28312548,36283236,46142811,58261125,73066305,91051857,112784399,138912059
%N 9th column of Catalan triangle A009766.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F a(n) = C(n,8)-C(n,6).
%F a(n) = A214292(n+15,7). - _Reinhard Zumkeller_, Jul 12 2012
%F From _Amiram Eldar_, Sep 06 2022: (Start)
%F Sum_{n>=15} 1/a(n) = 12515/11594583.
%F Sum_{n>=15} (-1)^(n+1)/a(n) = 1942528*log(2)/6435 - 60651032147/289864575. (End)
%p [seq(binomial(n,8)-binomial(n,6),n=15..45)];
%t 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 *)
%t 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 *)
%Y Cf. A009766, A214292.
%Y Cf. A064059, A064061, A124088.
%K easy,nonn
%O 15,1
%A _Zerinvary Lajos_, Nov 25 2006
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