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%I #19 Jan 31 2022 03:16:38
%S 1,18,247,3120,38221,462558,5570227,66940380,803772841,9647715498,
%T 115784793007,1389478551240,16674047790661,200090099366838,
%U 2401088821796587,28813104008531700,345757438837243681
%N Expansion of 1/((1-x)*(1-5*x)*(1-12*x)).
%H G. C. Greubel, <a href="/A016239/b016239.txt">Table of n, a(n) for n = 0..900</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (18,-77,60).
%F a(0)=1, a(1)=18; for n>1, a(n)=17*a(n-1)-60*a(n-2)+1. - _Vincenzo Librandi_, Feb 10 2011
%F a(n) = (4*12^(n+2) - 11*5^(n+2) + 7)/308. - _Yahia Kahloune_, Aug 13 2013
%F E.g.f.: (1/308)*(7*exp(x) - 275*exp(5*x) + 576*exp(12*x)). - _G. C. Greubel_, Jan 30 2022
%t LinearRecurrence[{18,-77,60}, {1,18,247}, 40] (* _G. C. Greubel_, Jan 30 2022 *)
%o (PARI) a(n) = (4*12^(n+2) - 11*5^(n+2) + 7)/308; \\ _Joerg Arndt_, Aug 13 2013
%o (Magma) [(4*12^(n+2) -11*5^(n+2) +7)/308: n in [0..40]]; // _G. C. Greubel_, Jan 30 2022
%o (Sage) [(4*12^(n+2) -11*5^(n+2) +7)/308 for n in (0..40)] # _G. C. Greubel_, Jan 30 2022
%Y Cf. A003463, A016238.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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