A021844 Expansion of 1/((1-x)*(1-4*x)*(1-6*x)*(1-12*x)).

1, 23, 363, 4963, 63539, 787731, 9609811, 116281811, 1401253587, 16850623699, 202422366419, 2430363281619, 29172151056595, 350112652220627, 4201633221810387, 50421288464357587, 605065606114711763, 7260848163537557715, 87130543395042760915, 1045568713702569416915

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• changed

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (23,-166,432,-288).

Programs

Mathematica

CoefficientList[Series[1/((1-x)(1-4x)(1-6x)(1-12x)),{x,0,40}],x] (* or *) LinearRecurrence[{23,-166,432,-288},{1,23,363,4963},40] (* Harvey P. Dale, May 11 2011 *)

PARI

Vec(1/((1-x)*(1-4*x)*(1-6*x)*(1-12*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

a(n) = 3*12^(n+1)/11 -3*6^(n+1)/5 +2^(2*n+2)/3 -1/165. - R. J. Mathar, Mar 15 2011

a(0)=1, a(1)=23, a(2)=363, a(3)=4963, a(n) = 23*a(n-1)-166*a(n-2)+432*a(n-3)-288*a(n-4). - Harvey P. Dale, May 11 2011