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 A020782 #24 Mar 26 2025 20:24:58
%S A020782 1,24,385,5160,62401,706104,7628545,79669320,810888001,8089258584,
%T A020782 79415935105,769621605480,7379461252801,70134974713464,
%U A020782 661651583000065,6203106293141640,57847125937972801,537010118353326744,4965807358070423425,45765395460943045800,420553385321258904001
%N A020782 Expansion of g.f. 1/((1-7*x)*(1-8*x)*(1-9*x)).
%H A020782 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (24,-191,504).
%F A020782 If we define f(m,j,x) = Sum_{k=j..m} (binomial(m,k)*stirling2(k,j)*x^(m-k)) then a(n-2) = f(n,2,7), (n>=2). - _Milan Janjic_, Apr 26 2009
%F A020782 From _Vincenzo Librandi_, Mar 15 2011: (Start)
%F A020782 a(n) = 24*a(n-1) - 191*a(n-2) + 504*a(n-3), n>=3.
%F A020782 a(n) = 17*a(n-1) - 72*a(n-2) + 7^n, n>=2. (End)
%F A020782 a(n) = 7^(n+2)/2 - 8^(n+2) + 9^(n+2)/2. - _R. J. Mathar_, Mar 15 2011
%F A020782 From _Elmo R. Oliveira_, Mar 26 2025: (Start)
%F A020782 E.g.f.: exp(7*x)*(49 - 128*exp(x) + 81*exp(2*x))/2.
%F A020782 a(n) = A005062(n+2) - A016149(n+1). (End)
%t A020782 CoefficientList[Series[1/((1-7x)(1-8x)(1-9x)),{x,0,20}],x] (* or *) LinearRecurrence[{24,-191,504},{1,24,385},20] (* _Harvey P. Dale_, Aug 20 2013 *)
%Y A020782 Cf. A005062, A016149.
%K A020782 nonn,easy
%O A020782 0,2
%A A020782 _N. J. A. Sloane_
%E A020782 More terms from _Elmo R. Oliveira_, Mar 26 2025