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 A016175 #28 Nov 14 2024 05:55:51
%S A016175 1,18,252,3240,40176,489888,5925312,71383680,858283776,10309483008,
%T A016175 123774262272,1485653944320,17830024114176,213973350064128,
%U A016175 2567758564933632,30813572964188160,369765696680165376,4437205286821429248,53246565001813819392,638959389381505843200,7667516328736510181376,92010217881788762554368
%N A016175 Expansion of 1/((1-6*x)*(1-12*x)).
%H A016175 G. C. Greubel, <a href="/A016175/b016175.txt">Table of n, a(n) for n = 0..920</a>
%H A016175 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-72).
%F A016175 a(n) = (6^n)*Stirling2(n+2, 2), n >= 0, with Stirling2(n, m) = A008277(n, m).
%F A016175 a(n) = 2*12^n - 6^n.
%F A016175 E.g.f.: (d^2/dx^2)((((exp(6*x)-1)/6)^2)/2!) = -exp(6*x) + 2*exp(12*x).
%F A016175 a(n) = 3^n*binomial(2^(n+1), 2). - Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009
%F A016175 a(n) = 12*a(n-1) + 6^n, n >= 1. - _Vincenzo Librandi_, Feb 09 2011
%F A016175 a(n) = 18*a(n-1) - 72*a(n-2), n >= 2. - _Vincenzo Librandi_, Feb 09 2011
%t A016175 Table[2*12^n -6^n, {n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 09 2011 *)
%t A016175 LinearRecurrence[{18,-72},{1,18},40] (* _Harvey P. Dale_, Nov 25 2013 *)
%o A016175 (PARI) Vec(1/((1-6*x)*(1-12*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o A016175 (Magma) [2*12^n - 6^n: n in [0..40]]; // _G. C. Greubel_, Nov 13 2024
%o A016175 (SageMath)
%o A016175 A016175= BinaryRecurrenceSequence(18,-72,1,18)
%o A016175 print([A016175(n) for n in range(41)]) # _G. C. Greubel_, Nov 13 2024
%Y A016175 Second column of triangle A075501.
%Y A016175 Cf. A016129, A075916.
%K A016175 nonn,easy
%O A016175 0,2
%A A016175 _N. J. A. Sloane_
%E A016175 More terms added by _G. C. Greubel_, Nov 13 2024