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 A016234 #33 May 05 2025 05:49:16
%S A016234 1,15,166,1650,15631,144585,1320796,11984820,108351661,977606355,
%T A016234 8810664226,79357013190,714518294491,6432190529325,57897344158456,
%U A016234 521114244398760,4690218934452121,42212924084385495,379921085131051486,3419313608037373530,30773941681625912551
%N A016234 Expansion of 1/((1-x) * (1-5*x) * (1-9*x)).
%H A016234 Harvey P. Dale, <a href="/A016234/b016234.txt">Table of n, a(n) for n = 0..1000</a>
%H A016234 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (15, -59, 45).
%F A016234 a(0)=1, a(1)=15, a(n) = 14*a(n-1) - 45*a(n-2) + 1. - _Vincenzo Librandi_, Feb 10 2011
%F A016234 a(n) = (9^(n+2) - 2*5^(n+2) + 1)/32. - _Yahia Kahloune_, Aug 13 2013
%F A016234 a(0)=1, a(1)=15, a(2)=166, a(n) = 15*a(n-1) - 59*a(n-2) + 45*a(n-3). - _Harvey P. Dale_, Oct 16 2014
%F A016234 O.g.f.: see the name.
%F A016234 E.g.f.: (d^2/dx^2) (exp(x)*((exp(4*x) - 1)^2)/(4^2*2!)) = exp(x)*(1 - 50*exp(4*x) + 81*exp(8*x))/32.
%F A016234 From _Seiichi Manyama_, May 05 2025: (Start)
%F A016234 a(n) = Sum_{k=0..n} 4^k * binomial(n+2,k+2) * Stirling2(k+2,2).
%F A016234 a(n) = Sum_{k=0..n} (-4)^k * 9^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2). (End)
%t A016234 CoefficientList[Series[1/((1-x)(1-5x)(1-9x)),{x,0,30}],x] (* or *) LinearRecurrence[{15,-59,45},{1,15,166},30] (* _Harvey P. Dale_, Oct 16 2014 *)
%o A016234 (PARI) Vec(1/((1-x)*(1-5*x)*(1-9*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o A016234 (PARI) a(n) = (9^(n+2) - 2*5^(n+2) + 1)/32; \\ _Joerg Arndt_, Aug 13 2013
%Y A016234 Cf. A000012, A003463.
%Y A016234 Cf. A016209, A016223, A016247.
%Y A016234 Cf. A016307, A018054.
%K A016234 nonn,easy
%O A016234 0,2
%A A016234 _N. J. A. Sloane_