This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A016164 #29 Nov 10 2024 08:59:06
%S A016164 1,15,175,1875,19375,196875,1984375,19921875,199609375,1998046875,
%T A016164 19990234375,199951171875,1999755859375,19998779296875,
%U A016164 199993896484375,1999969482421875,19999847412109375,199999237060546875
%N A016164 Expansion of 1/((1-5*x)*(1-10*x)).
%H A016164 G. C. Greubel, <a href="/A016164/b016164.txt">Table of n, a(n) for n = 0..994</a>
%H A016164 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (15,-50).
%F A016164 a(n) = (5^n)*Stirling2(n+2, 2), n >= 0, with Stirling2(n, m) = A008277(n, m).
%F A016164 a(n) = -5^n + 2*10^n.
%F A016164 G.f.: 1/((1-5*x)*(1-10*x)).
%F A016164 E.g.f.: (d^2/dx^2)((((exp(5*x)-1)/5)^2)/2!) = -exp(5*x) + 2*exp(10*x).
%F A016164 Sum_{k=1..n} 5^(k-1)*5^(n-k)*binomial(n, k). - _Zerinvary Lajos_, Sep 24 2006
%F A016164 a(0)=1, a(n) = 10*a(n-1) + 5^n. - _Vincenzo Librandi_, Feb 09 2011
%t A016164 Table[5^n*(2^(n+1)-1), {n,0,30}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 01 2011 *)
%t A016164 LinearRecurrence[{15,-50},{1,15},20] (* _Harvey P. Dale_, Aug 08 2023 *)
%o A016164 (PARI) Vec(1/((1-5*x)(1-10*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 25 2012
%o A016164 (Magma) [n le 2 select 15^(n-1) else 15*Self(n-1) -50*Self(n-2): n in [1..31]]; // _G. C. Greubel_, Nov 09 2024
%o A016164 (SageMath)
%o A016164 A016164=BinaryRecurrenceSequence(15,-50,1,15)
%o A016164 [A016164(n) for n in range(31)] # _G. C. Greubel_, Nov 09 2024
%Y A016164 Second column of triangle A075500.
%Y A016164 Cf. A008277, A016161, A075911.
%K A016164 nonn,easy
%O A016164 0,2
%A A016164 _N. J. A. Sloane_