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%I #13 Sep 03 2019 03:38:39
%S 1,5,150,2000,35000,550000,9000000,145000000,2350000000,38000000000,
%T 615000000000,9950000000000,161000000000000,2605000000000000,
%U 42150000000000000,682000000000000000,11035000000000000000
%N Expansion of (1-5x)/(1-10x-100x^2).
%C 2*a(n)/10^n = A000032(n). Fifth binomial transform of 1, 0, 125, 0, 15625, ...
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,100).
%F a(n) = (5 + 5*sqrt(5))^n/2 + (5 - 5*sqrt(5))^n/2.
%t CoefficientList[Series[(1-5x)/(1-10x-100x^2),{x,0,30}],x] (* or *) LinearRecurrence[{10,100},{1,5},30] (* _Harvey P. Dale_, Aug 27 2019 *)
%Y Cf. A000032 (Lucas numbers).
%K easy,nonn
%O 0,2
%A _Paul Barry_, Apr 26 2004
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