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 A020726 #37 Mar 26 2025 18:29:28
%S A020726 1,27,493,7599,106645,1411431,17955757,222093423,2690508229,
%T A020726 32080473975,377794514461,4405195463487,50953884924853,
%U A020726 585473143132359,6690087028209805,76090252032830991,861988540696279717,9731848557669909783,109550181794434004989,1230051085699164039135
%N A020726 Expansion of g.f. 1/((1-6*x)*(1-10*x)*(1-11*x)).
%H A020726 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (27,-236,660).
%F A020726 a(n) = 21*a(n-1) - 110*a(n-2) + 6^n for n>1, a(0)=1, a(1)=27. - _Vincenzo Librandi_, Mar 11 2011
%F A020726 a(n) = (4*11^(n+2) - 5*10^(n+2) + 6^(n+2))/20. - _Yahia Kahloune_, Jun 30 2013
%F A020726 In general, for the expansion of 1/((1-r*x)(1-s*x)(1-t*x)) with t > s > r, we have the formula: a(n) = ((s-r)*t^(n+2) - (t-r)*s^(n+2) + (t-s)*r^(n+2))/((s-r)*(t-r)*(t-s)). - _Yahia Kahloune_, Sep 09 2013
%F A020726 a(0) = 1, a(1) = 27, a(2) = 493, a(n) = 27*a(n-1) - 236*a(n-2) + 660*a(n-3). - _Harvey P. Dale_, Oct 01 2014
%F A020726 From _Elmo R. Oliveira_, Mar 26 2025: (Start)
%F A020726 E.g.f.: exp(6*x)*(484*exp(5*x) - 500*exp(4*x) + 36)/20.
%F A020726 a(n) = A016174(n+1) - A016173(n+1). (End)
%t A020726 CoefficientList[Series[1/((1-6x)(1-10x)(1-11x)),{x,0,30}],x] (* or *) LinearRecurrence[{27,-236,660},{1,27,493},30] (* _Harvey P. Dale_, Oct 01 2014 *)
%o A020726 (PARI) Vec(1/((1-6*x)*(1-10*x)*(1-11*x)) + O(x^30)) \\ _Jinyuan Wang_, Mar 10 2020
%Y A020726 Cf. A016173, A016174.
%K A020726 nonn,easy
%O A020726 0,2
%A A020726 _N. J. A. Sloane_
%E A020726 More terms from _Elmo R. Oliveira_, Mar 26 2025