A021684 Expansion of 1/((1-x)(1-3x)(1-9x)(1-10x)).

1, 23, 360, 4810, 59111, 690573, 7801990, 86089520, 933531621, 9989073523, 105774639620, 1110701801430, 11583617458531, 120125571974873, 1239860303429250, 12746044308940540, 130587414625807841

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,-169,417,-270)

Programs

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 9 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 11 2013 *)
LinearRecurrence[{23,-169,417,-270},{1,23,360,4810},30] (* Harvey P. Dale, Nov 18 2018 *)

PARI

Vec(1/((1-x)*(1-3*x)*(1-9*x)*(1-10*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

a(n) = -1/144 +10^(n+3)/63+3^(n+2)/28 -3*9^(n+2)/16. - R. J. Mathar, Mar 15 2011