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Expansion of 1/((1-2*x)*(1-6*x)*(1-8*x)*(1-12*x)).
1

%I #21 Sep 08 2022 08:44:49

%S 1,28,516,7952,111440,1477056,18912832,236879104,2924469504,

%T 35764112384,434623874048,5259666886656,63472710995968,

%U 764545789837312,9197653087371264,110557371200503808,1328176959287263232,15950056940486000640,191496303058077614080

%N Expansion of 1/((1-2*x)*(1-6*x)*(1-8*x)*(1-12*x)).

%H G. C. Greubel, <a href="/A026738/b026738.txt">Table of n, a(n) for n = 0..915</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (28,-268,1008,-1152).

%F a(n) = (18*12^(n + 1) - 5*8^(n + 2) + 135*6^n - 2^n)/30. - _R. J. Mathar_, Jun 23 2013

%F a(0) = 1, a(1)=28, a(2)=516, a(3)=7952, a(n) = 28*a(n-1) - 268*a(n-2) + 1008*a(n-3) - 1152*a(n-4). - _Harvey P. Dale_, Jul 25 2013

%F E.g.f.: (-exp(2*x) + 135*exp(6*x) - 320*exp(8*x) + 216*exp(12*x))/30. - _G. C. Greubel_, Oct 26 2019

%p A026738:= n-> (18*12^(n+1) -5*8^(n+2) +135*6^n -2^n)/30: seq(A026738(n), n=0..30); # _Wesley Ivan Hurt_, Feb 15 2014

%t CoefficientList[Series[1/((1-2x)(1-6x)(1-8x)(1-12x)),{x,0,30}],x] (* or *) LinearRecurrence[{28,-268,1008,-1152},{1,28,516,7952},30] (* _Harvey P. Dale_, Jul 25 2013 *)

%o (PARI) vector(31, n, (18*12^n -5*8^(n+1) +135*6^(n-1) -2^(n-1))/30) \\ _G. C. Greubel_, Oct 26 2019

%o (Magma) [(18*12^(n+1) -5*8^(n+2) +135*6^n -2^n)/30: n in [0..30]]; // _G. C. Greubel_, Oct 26 2019

%o (Sage) [(18*12^(n+1) -5*8^(n+2) +135*6^n -2^n)/30 for n in (0..30)] # _G. C. Greubel_, Oct 26 2019

%o (GAP) List([0..30], n-> (18*12^(n+1) -5*8^(n+2) +135*6^n -2^n)/30); # _G. C. Greubel_, Oct 26 2019

%K nonn

%O 0,2

%A _N. J. A. Sloane_