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 A016178 #30 Jul 23 2024 14:51:04
%S A016178 1,16,193,2080,21121,206896,1979713,18640960,173533441,1602154576,
%T A016178 14701866433,134294124640,1222488408961,11099284691056,
%U A016178 100571785292353,909893629141120,8222275592839681,74233110849544336,669726411243809473,6038936596379658400,54430221633714537601
%N A016178 Expansion of g.f. 1/((1 - 7x)*(1 - 9x)).
%H A016178 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-63).
%F A016178 a(n) = (9^(n+1) - 7^(n+1))/2 = A081202(n+1). Binomial transform of A081034. - _R. J. Mathar_, Sep 18 2008
%F A016178 From _Vincenzo Librandi_, Feb 09 2011: (Start)
%F A016178 a(n) = 9*a(n-1) + 7^n, with a(0)=1.
%F A016178 a(n) = 16*a(n-1) - 63*a(n-2), n >= 2. (End)
%F A016178 E.g.f.: exp(7*x)*(9*exp(2*x) - 7)/2. - _Stefano Spezia_, Jul 23 2024
%t A016178 Join[{a=1,b=16},Table[c=16*b-63*a;a=b;b=c,{n,40}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 08 2011 *)
%t A016178 CoefficientList[Series[1/((1-7x)(1-9x)),{x,0,30}],x] (* or *) LinearRecurrence[ {16,-63},{1,16},30] (* _Harvey P. Dale_, Mar 11 2013 *)
%o A016178 (PARI) a(n)=(9^n++-7^n)/2 \\ _Charles R Greathouse IV_, Sep 24 2012
%Y A016178 Cf. A081034, A081202.
%K A016178 nonn,easy
%O A016178 0,2
%A A016178 _N. J. A. Sloane_
%E A016178 a(18)-a(20) from _Stefano Spezia_, Jul 23 2024