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%I #22 Sep 08 2022 08:45:00
%S 1,10,175,2500,38125,568750,8546875,128125000,1922265625,28832031250,
%T 432490234375,6487304687500,97309814453125,1459645996093750,
%U 21894696044921875,328420410156250000,4926306304931640625,73894593811035156250,1108418910980224609375
%N Expansion of 1/((1+5*x)*(1-15*x)).
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H G. C. Greubel, <a href="/A053537/b053537.txt">Table of n, a(n) for n = 0..845</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,75).
%F a(n) = (5^n/4)*(3^(n+1) + (-1)^n).
%F a(n) = 10*a(n-1) + 75*a(n-2), with a(0)=1, a(1)=10.
%F E.g.f.: (3*exp(15*x) + exp(-5*x))/4. - _G. C. Greubel_, May 16 2019
%t LinearRecurrence[{10, 75}, {1, 10}, 30] (* _G. C. Greubel_, May 16 2019 *)
%t CoefficientList[Series[1/((1+5x)(1-15x)),{x,0,20}],x] (* _Harvey P. Dale_, Jun 15 2022 *)
%o (PARI) Vec(1/((1+5*x)*(1-15*x)) + O(x^30)) \\ _Michel Marcus_, Dec 03 2014
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/((1+5*x)*(1-15*x)) )); // _G. C. Greubel_, May 16 2019
%o (Sage) (1/((1+5*x)*(1-15*x))).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 16 2019
%o (GAP) a:=[1,10];; for n in [3..30] do a[n]:=10*a[n-1]+75*a[n-2]; od; a; # _G. C. Greubel_, May 16 2019
%Y Cf. A015518.
%K easy,nonn
%O 0,2
%A _Barry E. Williams_, Jan 15 2000
%E Terms a(11) onward added by _G. C. Greubel_, May 16 2019
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