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%I #23 Sep 08 2022 08:44:41
%S 1,15,157,1419,11869,94731,733069,5551323,41378557,304766187,
%T 2224062061,16112628987,116053574365,831966057483,5941308640333,
%U 42294437942811,300292730428093,2127439102098219,15044413649559085
%N Expansion of 1/((1-2*x)*(1-6*x)*(1-7*x)).
%H Vincenzo Librandi, <a href="/A016304/b016304.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (15,-68,84)
%F a(n) = (7^(n+2) - 2^(n+2))/5-(6^(n+2) - 2^(n+2))/4. - _Zerinvary Lajos_, Jun 05 2009 [corrected by _Joerg Arndt_, Aug 25 2011]
%F From Vincenzo Librandi_, Aug 25 2011: (Start)
%F a(0)=1, a(1)=15, a(2)=157, a(n) = 15*a(n-1) - 68*a(n-2) + 84*a(n-3);
%F a(0)=1, a(1)=15, a(n) = 13*a(n-1) - 42*a(n-2) + 2^n. (End)
%t CoefficientList[Series[1/((1-2x)(1-6x)(1-7x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{15, -68, 84}, {1, 15, 157}, 30]
%o (Sage) [(7^n - 2^n)/5-(6^n - 2^n)/4 for n in range(2,21)] # _Zerinvary Lajos_, Jun 05 2009
%o (Magma) [ n eq 1 select 1 else n eq 2 select 15 else n eq 3 select 157 else 15*Self(n-1)-68*Self(n-2) +84*Self(n-3): n in [1..20] ]; // _Vincenzo Librandi_, Aug 25 2011
%o (PARI) Vec(1/((1-2*x)*(1-6*x)*(1-7*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y Cf. A016129, A016130, A016311, A016316, A016321, A016325. - _Zerinvary Lajos_, Jun 05 2009
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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