A025931 Expansion of 1/((1-2x)(1-3x)(1-5x)(1-7x)).

1, 17, 188, 1726, 14343, 112371, 848506, 6255392, 45386165, 325753285, 2320698744, 16447547298, 116147697667, 818112983159, 5752200695702, 40392496919044, 283383067688049, 1986859807248393, 13923911479636180, 97546847987676230, 683225284523104511

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (17,-101,247,-210)

Crossrefs

Column k=4 of A343751.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1,
     `if`(k=0, 0, ithprime(k)*b(n-1, k)+b(n, k-1)))
    end:
a:= n-> b(n, 4):
seq(a(n), n=0..28);  # Alois P. Heinz, Jul 14 2021

Mathematica

CoefficientList[Series[1/((1-2x)(1-3x)(1-5x)(1-7x)),{x,0,20}],x] (* or *) LinearRecurrence[{17,-101,247,-210},{1,17,188,1726},20] (* Harvey P. Dale, Aug 05 2013 *)

Formula

a(n) = 12*a(n-1) - 35*a(n-2) + 3^(n+1) - 2^(n+1), n >= 2. - Vincenzo Librandi, Mar 19 2011

a(n) = 7^(n+3)/40 - 2^(n+3)/15 + 3^(n+3)/8 - 5^(n+3)/12. - R. J. Mathar, Mar 19 2011