A091903 Expansion of x/((1+5x)(1-10x)).

0, 1, 5, 75, 625, 6875, 65625, 671875, 6640625, 66796875, 666015625, 6669921875, 66650390625, 666748046875, 6666259765625, 66668701171875, 666656494140625, 6666717529296875, 66666412353515625, 666667938232421875

Offset: 0

Author

Paul Barry, Feb 10 2004

Keywords

• easy
• nonn

Comments

a(n)=A091883(n+1)/50; a(n)/a(n+1)->1/10.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,50).

Programs

Mathematica

CoefficientList[Series[x/((1+5x)(1-10x)),{x,0,30}],x] (* or *) LinearRecurrence[ {5,50},{0,1},30] (* Harvey P. Dale, Mar 13 2013 *)

Formula

a(n)=10^n/15-(-5)^n/15

a(0)=0, a(1)=1, a(n)=5*a(n-1)+50*a(n-2). - Harvey P. Dale, Mar 13 2013

a(n) = 5^(n-1)*A001045(n). - R. J. Mathar, Mar 08 2021