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 A270369 #37 Mar 25 2025 19:45:21
%S A270369 1,2,18,162,1458,13122,118098,1062882,9565938,86093442,774840978,
%T A270369 6973568802,62762119218,564859072962,5083731656658,45753584909922,
%U A270369 411782264189298,3706040377703682,33354363399333138,300189270593998242,2701703435345984178,24315330918113857602,218837978263024718418
%N A270369 Expansion of g.f. (1-7*x)/(1-9*x).
%H A270369 Colin Barker, <a href="/A270369/b270369.txt">Table of n, a(n) for n = 0..1000</a>
%H A270369 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (9).
%F A270369 G.f.: (1-7*x)/(1-9*x).
%F A270369 a(n) = 9*a(n-1) for n>1.
%F A270369 a(n) = 2*9^(n-1) for n>0.
%F A270369 From _Amiram Eldar_, May 08 2023: (Start)
%F A270369 Sum_{n>=0} 1/a(n) = 25/16.
%F A270369 Sum_{n>=0} (-1)^n/a(n) = 11/20.
%F A270369 Product_{n>=1} (1 - 1/a(n)) = A132025. (End)
%F A270369 E.g.f.: (2*exp(9*x) + 7)/9. - _Elmo R. Oliveira_, Mar 25 2025
%t A270369 CoefficientList[Series[(1-7x)/(1-9x),{x,0,20}],x] (* or *) Join[ {1}, NestList[9#&,2,20]] (* _Harvey P. Dale_, Oct 15 2017 *)
%o A270369 (PARI) Vec((1-7*x)/(1-9*x) + O(x^30))
%Y A270369 Cf. A001019 (powers of 9), A054879 (partial sums), A132025.
%Y A270369 Cf. similar sequences with g.f. (1-k*x)/(1-9*x) and k=0..8: A001019 (k=0; k=8 gives two initial 1's ), A055275 (k=1), A270472 (k=2), A092810 (k=3), A067403 (k=4), A270473 (k=5), A102518 (k=6), this sequence (k=7).
%K A270369 nonn,easy
%O A270369 0,2
%A A270369 _Colin Barker_, Mar 18 2016