A022343 Expansion of 1/((1-x)*(1-5*x)*(1-6*x)*(1-10*x)).

1, 22, 323, 4004, 45465, 491106, 5149327, 53020528, 539857109, 5458923470, 54963556011, 551942523132, 5533572185233, 55422129454714, 554747369555975, 5550668292585416, 55526041242871437, 555377516005134438

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..995
• Index entries for linear recurrences with constant coefficients, signature (22,-161,440,-300).

Programs

Mathematica

Table[(1/180)*(9*5^(n + 3) + 10^(n + 3) - 9*6^(n + 3) - 1), {n,0,50}] (* G. C. Greubel, Aug 25 2017 *)
CoefficientList[Series[1/((1-x)(1-5x)(1-6x)(1-10x)),{x,0,30}],x] (* or *) LinearRecurrence[{22,-161,440,-300},{1,22,323,4004},30] (* Harvey P. Dale, Aug 18 2018 *)

PARI

Vec(1/(1-x)/(1-5*x)/(1-6*x)/(1-10*x)+O(x^99)) \\ Charles R Greathouse IV, Dec 22 2011

Formula

a(n) = (1/180)*(9*5^(n+3) + 10^(n+3) - 9*6^(n+3) - 1). - R. J. Mathar, Mar 11 2011

a(n) = 16*a(n-1) - 60*a(n-2) + (5^(n+1) - 1)/4, n>=2. - Vincenzo Librandi, Mar 12 2011

E.g.f.: (1/180)*(- exp(x) + 1125*exp(5*x) - 1944*exp(6*x) + 1000*exp(10*x)). - G. C. Greubel, Aug 25 2017