A021664 Expansion of 1/((1-x)(1-3x)(1-8x)(1-11x)).

1, 23, 362, 4894, 61251, 733461, 8546764, 97847228, 1106991941, 12422320339, 138608884206, 1540404875802, 17070111627271, 188776494239057, 2084583574516688, 22994756444303416, 253457017948866441

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (23,-167,409,-264)

Programs

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 8 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 11 2013 *)
LinearRecurrence[{23, -167, 409, -264}, {1, 23, 362, 4894}, 20] (* Harvey P. Dale, Feb 17 2015 *)

PARI

Vec(1/((1-x)*(1-3*x)*(1-8*x)*(1-11*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

a(n) = 3^(n+3)/80 -1/140 +11^(n+3)/240 -8^(n+3)/105. - R. J. Mathar, Mar 15 2011

a(0) = 1, a(1) = 23, a(2) = 362, a(3) = 4894, a(n) = 23*a(n-1) - 167*a(n-2) + 409*a(n-3) - 264*a(n-4). - Harvey P. Dale, Feb 17 2015