A099111 Expansion of 1 / ((1+x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)).

1, 13, 112, 798, 5103, 30471, 173734, 958936, 5170165, 27396369, 143295516, 742128114, 3814432987, 19490910907, 99140278258, 502476527532, 2539579950369, 12806979393285, 64472086878760, 324111808432390

Offset: 0

Author

Ralf Stephan, Sep 28 2004

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (13, -57, 83, 34, -120).

Crossrefs

First differences are in A004058. Pairwise sums are in A025211.

Programs

Magma

[(1/360)*(6250*5^n - 9216*4^n + 3645*3^n - 320*2^n + (-1)^n): n in [0..20]]; // Vincenzo Librandi, Oct 11 2011

Mathematica

CoefficientList[Series[1/((1+x)(1-2x)(1-3x)(1-4x)(1-5x)),{x,0,20}],x] (* or *) LinearRecurrence[{13,-57,83,34,-120},{1,13,112,798,5103},20] (* Harvey P. Dale, Jan 17 2024 *)

Formula

a(n) = (1/360)*(6250*5^n - 9216*4^n + 3645*3^n - 320*2^n + (-1)^n).