A169797 Expansion of ((1-x)/(1-2x))^10.

1, 10, 65, 340, 1550, 6412, 24650, 89440, 309605, 1030490, 3317445, 10377180, 31655820, 94451520, 276313200, 794169792, 2246410560, 6262748160, 17230138880, 46831339520, 125870737408, 334826700800, 882159984640, 2303540756480, 5965195018240, 15327324667904

Offset: 0

Author

N. J. A. Sloane, May 15 2010

Keywords

• nonn
• easy

Comments

a(n) is the number of weak compositions of n with exactly 9 parts equal to 0. - Milan Janjic, Jun 27 2010

Links

• Nickolas Hein, Jia Huang, Variations of the Catalan numbers from some nonassociative binary operations, arXiv:1807.04623 [math.CO], 2018.
• M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.
• M. Janjic, B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014) # 14.3.5.
• Index entries for linear recurrences with constant coefficients, signature (20,-180,960,-3360,8064,-13440,15360,-11520,5120,-1024)

Crossrefs

((1-x)/(1-2x))^k: A011782, A045623, A058396, A062109, A169792-A169797; a row of A160232.

Programs

Mathematica

CoefficientList[Series[((1-x)/(1-2x))^10,{x,0,30}],x] (* or *) Join[ {1}, LinearRecurrence[{20,-180,960,-3360,8064,-13440,15360,-11520,5120,-1024},{10,65,340,1550,6412,24650,89440,309605,1030490,3317445},30]] (* Harvey P. Dale, Aug 21 2014 *)

PARI

Vec(((1-x)/(1-2*x))^10+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012

Formula

a(n) = 2^(n-17)*(n+11) *(n^8 + 124*n^7 + 5986*n^6 + 143944*n^5 + 1836529*n^4 + 12358156*n^3 + 42005484*n^2 + 64730736*n + 33747840)/2835, n > 0. - R. J. Mathar, Mar 14 2011