A091903 - OEIS

%I #11 Mar 08 2021 12:24:12

%S 0,1,5,75,625,6875,65625,671875,6640625,66796875,666015625,6669921875,

%T 66650390625,666748046875,6666259765625,66668701171875,

%U 666656494140625,6666717529296875,66666412353515625,666667938232421875

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

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

%H Harvey P. Dale, <a href="/A091903/b091903.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,50).

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

%F a(0)=0, a(1)=1, a(n)=5*a(n-1)+50*a(n-2). - _Harvey P. Dale_, Mar 13 2013

%F a(n) = 5^(n-1)*A001045(n). - _R. J. Mathar_, Mar 08 2021

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

%K easy,nonn

%O 0,3

%A _Paul Barry_, Feb 10 2004