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

17,1

Links

Table of n, a(n) for n=17..43.

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

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)

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 *)

Crossrefs

Cf. A009766, A214292.

Cf. A064059, A064061, A124087.

Sequence in context: A331664 A031826 A243835 * A244106 A264182 A258496

Adjacent sequences: A124085 A124086 A124087 * A124089 A124090 A124091

Keyword

easy,nonn

Author

Zerinvary Lajos, Nov 25 2006

Status

approved