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%I #21 Aug 08 2023 15:00:27
%S 1,15,175,1875,19375,196875,1984375,19921875,199609375,1998046875,
%T 19990234375,199951171875,1999755859375,19998779296875,
%U 199993896484375,1999969482421875,19999847412109375,199999237060546875
%N Expansion of 1/((1-5x)(1-10x)).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (15, -50).
%F a(n) = (5^n)*Stirling2(n+2, 2), n >= 0, with Stirling2(n, m) = A008277(n, m).
%F a(n) = -5^n + 2*10^n.
%F G.f.: 1/((1-5*x)*(1-10*x)).
%F E.g.f.: (d^2/dx^2)((((exp(5*x)-1)/5)^2)/2!) = -exp(5*x) + 2*exp(10*x).
%F Sum_{k=1..n} 5^(k-1)*5^(n-k)*binomial(n, k). - _Zerinvary Lajos_, Sep 24 2006
%F a(0)=1, a(n) = 10*a(n-1) + 5^n. - _Vincenzo Librandi_, Feb 09 2011
%t Join[{a=1,b=15},Table[c=15*b-50*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 01 2011 *)
%t LinearRecurrence[{15,-50},{1,15},20] (* _Harvey P. Dale_, Aug 08 2023 *)
%o (PARI) Vec(1/((1-5*x)(1-10*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 25 2012
%Y Second column of triangle A075500.
%Y Cf. A075911.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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