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%I #16 Sep 06 2022 02:58:03
%S 4862,16796,41990,90440,177650,326876,572033,961400,1562275,2466750,
%T 3798795,5722860,8454225,12271350,17530500,24682944,34295052,47071640,
%U 63882940,85795600,114108148,150391384,196534195,254795320,327861625,418913482,531697881
%N 10th column of Catalan triangle A009766.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F a(n) = C(n,9)-C(n,7).
%F a(n) = A214292(n+17,8). - _Reinhard Zumkeller_, Jul 12 2012
%F From _Amiram Eldar_, Sep 06 2022: (Start)
%F Sum_{n>=17} 1/a(n) = 2074783/6618932320.
%F Sum_{n>=17} (-1)^(n+1)/a(n) = 2259208566291/4727808800 - 8379648*log(2)/12155. (End)
%p [seq(binomial(n,9)-binomial(n,7),n=17..42)];
%t CoefficientList[Series[(1430*z^8 - 12870*z^7 + 51051*z^6 - 116688*z^5 + 168300*z^4 - 157080*z^3 + 92820*z^2 - 31824*z + 4862)/(z - 1)^10, {z, 0, 100}], z] (* _Vladimir Joseph Stephan Orlovsky_, Jul 16 2011 *)
%Y Cf. A009766, A214292.
%Y Cf. A064059, A064061, A124087.
%K easy,nonn
%O 17,1
%A _Zerinvary Lajos_, Nov 25 2006
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