A028219 - OEIS

%I #23 Sep 08 2022 08:44:50

%S 1,39,961,19131,336217,5446035,83308177,1221791547,17352006793,

%T 240304555491,3261449180353,43542585627723,573464912457529,

%U 7467052092622707,96294712139682289,1231626797709018459

%N Expansion of 1/((1 - 6*x)*(1 - 10*x)*(1 - 11*x)*(1 - 12*x)).

%H G. C. Greubel, <a href="/A028219/b028219.txt">Table of n, a(n) for n = 0..900</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (39,-560,3492,-7920).

%F a(n) = 23*a(n-1) - 132*a(n-2) + 2^(n-1)*(5^(n+1) - 3^(n+1)), n >= 2. - _Vincenzo Librandi_, Mar 13 2011

%F a(n) = (5*12^(n+2) - 11^(n+3) + 5^4*10^n - 9*6^n)/5. - _R. J. Mathar_, Mar 15 2011

%F E.g.f.: (720*exp(12*x) -1331*exp(11*x) + 625*exp(10*x) -9*exp(6*x))/5. - _G. C. Greubel_, Oct 28 2019

%p seq((5*12^(n+2) + 5^4*10^n - 9*6^n - 11^(n+3))/5, n=0..30); # _G. C. Greubel_, Oct 28 2019

%t CoefficientList[Series[1/((1 - 6x)(1 - 10x)(1 - 11x)(1 - 12x))  , {x, 0, 29}], x] (* _Alonso del Arte_, Oct 25 2019 *)

%o (PARI) vector(31, n, (5*12^(n+1) +5^4*10^(n-1) -9*6^(n-1) -11^(n+2))/5) \\ _G. C. Greubel_, Oct 28 2019

%o (Magma) [(5*12^(n+2) + 5^4*10^n - 9*6^n - 11^(n+3))/5: n in [0..30]]; // _G. C. Greubel_, Oct 28 2019

%o (Sage) [(5*12^(n+2) + 5^4*10^n - 9*6^n - 11^(n+3))/5 for n in (0..30)] # _G. C. Greubel_, Oct 28 2019

%o (GAP) List([0..30], n-> (5*12^(n+2) + 5^4*10^n - 9*6^n - 11^(n+3))/5); # _G. C. Greubel_, Oct 28 2019

%K nonn

%O 0,2

%A _N. J. A. Sloane_