A028130 Expansion of 1/((1-4x)(1-6x)(1-7x)(1-8x)).
1, 25, 395, 5045, 56931, 592725, 5834515, 55132165, 505157411, 4519668725, 39685517235, 343261312485, 2933027514691, 24811827085525, 208162421081555, 1734382406904005, 14367095262780771, 118431759773683125
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (25,-230,920,-1344).
Programs
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Mathematica
CoefficientList[Series[1/((1-4x)(1-6x)(1-7x)(1-8x)),{x,0,30}],x] (* or *) LinearRecurrence[{25,-230,920,-1344},{1,25,395,5045},30] (* Harvey P. Dale, Jun 19 2014 *) -
PARI
Vec(1/((1-4*x)*(1-6*x)*(1-7*x)*(1-8*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012
Formula
From Vincenzo Librandi, Mar 17 2011: (Start)
a(n) = 25*a(n-1) - 230*a(n-2) + 920*a(n-3) - 1344*a(n-4), n >= 4.
a(n) = 15*a(n-1) - 56*a(n-2) - 2*4^n + 3*6^n, n >= 2. (End)
a(n) = -7^(n+3)/3 - 2*4^(n+1)/3 + 9*6^(n+1) + 8^(n+2). - R. J. Mathar, Mar 18 2011