A124088 10th column of Catalan triangle A009766.
4862, 16796, 41990, 90440, 177650, 326876, 572033, 961400, 1562275, 2466750, 3798795, 5722860, 8454225, 12271350, 17530500, 24682944, 34295052, 47071640, 63882940, 85795600, 114108148, 150391384, 196534195, 254795320, 327861625, 418913482, 531697881
Offset: 17
Links
- Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
Programs
-
Maple
[seq(binomial(n,9)-binomial(n,7),n=17..42)];
-
Mathematica
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 *)
Formula
a(n) = C(n,9)-C(n,7).
a(n) = A214292(n+17,8). - Reinhard Zumkeller, Jul 12 2012
From Amiram Eldar, Sep 06 2022: (Start)
Sum_{n>=17} 1/a(n) = 2074783/6618932320.
Sum_{n>=17} (-1)^(n+1)/a(n) = 2259208566291/4727808800 - 8379648*log(2)/12155. (End)