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%I A016175 #23 Jan 09 2018 03:00:18
%S A016175 1,18,252,3240,40176,489888,5925312,71383680,858283776,10309483008,
%T A016175 123774262272,1485653944320,17830024114176,213973350064128,
%U A016175 2567758564933632,30813572964188160,369765696680165376
%N A016175 Expansion of 1/((1-6x)(1-12x)).
%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) = -6^n + 2*12^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-1) = ((9+sqrt9)^n - (9-sqrt9)^n)/6. - 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 Join[{a=1,b=18},Table[c=18*b-72*a;a=b;b=c,{n,40}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 09 2011 *)
%t A016175 LinearRecurrence[{18,-72},{1,18},20] (* _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
%Y A016175 Second column of triangle A075501.
%Y A016175 Cf. A075916.
%K A016175 nonn,easy
%O A016175 0,2
%A A016175 _N. J. A. Sloane_

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