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 A270567 #19 Mar 25 2025 20:26:40
%S A270567 1,9,45,225,1125,5625,28125,140625,703125,3515625,17578125,87890625,
%T A270567 439453125,2197265625,10986328125,54931640625,274658203125,
%U A270567 1373291015625,6866455078125,34332275390625,171661376953125,858306884765625,4291534423828125,21457672119140625,107288360595703125
%N A270567 Expansion of g.f. (1+4*x)/(1-5*x).
%C A270567 Partial sums are 1, 10, 55, 280, 1405, 7030, ...
%C A270567 Apparently a duplicate of A189274. - _R. J. Mathar_, May 13 2016
%H A270567 Colin Barker, <a href="/A270567/b270567.txt">Table of n, a(n) for n = 0..1000</a>
%H A270567 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (5).
%F A270567 G.f.: (1+4*x)/(1-5*x).
%F A270567 a(n) = 5*a(n-1) for n>1.
%F A270567 a(n) = 9*5^(n-1) for n>0.
%F A270567 E.g.f.: (9*exp(5*x) - 4)/5. - _Elmo R. Oliveira_, Mar 25 2025
%t A270567 CoefficientList[Series[(1 + 4 x)/(1 - 5 x), {x, 0, 23}], x] (* _Michael De Vlieger_, Mar 19 2016 *)
%o A270567 (PARI) Vec((1+4*x)/(1-5*x) + O(x^30))
%Y A270567 Cf. A000351 (powers of 5), A128625 (1+3*x)/(1-5*x), A189274.
%K A270567 nonn,easy
%O A270567 0,2
%A A270567 _Colin Barker_, Mar 19 2016