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Expansion of 1/((1-x)*(1-x^4)*(1-x^6)*(1-x^12)).
1

%I #21 Sep 08 2022 08:44:36

%S 1,1,1,1,2,2,3,3,4,4,5,5,8,8,9,9,12,12,15,15,18,18,21,21,27,27,30,30,

%T 36,36,42,42,48,48,54,54,64,64,70,70,80,80,90,90,100,100,110,110,125,

%U 125,135,135,150,150,165,165,180,180,195,195,216,216,231,231,252,252,273,273,294

%N Expansion of 1/((1-x)*(1-x^4)*(1-x^6)*(1-x^12)).

%H Vincenzo Librandi, <a href="/A008719/b008719.txt">Table of n, a(n) for n = 0..1000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=242">Encyclopedia of Combinatorial Structures 242</a>

%H <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 1, -1, 1, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 1, -1, 1, 0, 0, 1, -1).

%p seq(coeff(series(1/((1-x)*(1-x^4)*(1-x^6)*(1-x^12)), x, n+1), x, n), n = 0..70); # _G. C. Greubel_, Sep 09 2019

%t CoefficientList[Series[1/((1-x)(1-x^4)(1-x^6)(1-x^12)), {x,0,70}], x] (* _Vincenzo Librandi_, Jun 23 2013 *)

%t LinearRecurrence[{1,0,0,1,-1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,-1,1,0,0,1,-1},{1,1,1,1,2,2,3,3,4,4,5,5,8,8,9,9,12,12,15,15,18,18,21},80] (* _Harvey P. Dale_, Apr 03 2022 *)

%o (PARI) my(x='x+O('x^70)); Vec(1/((1-x)*(1-x^4)*(1-x^6)*(1-x^12))) \\ _G. C. Greubel_, Sep 09 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/((1-x)*(1-x^4)*(1-x^6)*(1-x^12)) )); // _G. C. Greubel_, Sep 09 2019

%o (Sage)

%o def A008719_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P(1/((1-x)*(1-x^4)*(1-x^6)*(1-x^12))).list()

%o A008719_list(70) # _G. C. Greubel_, Sep 09 2019

%K nonn,easy

%O 0,5

%A _N. J. A. Sloane_

%E Typo in name fixed by _Vincenzo Librandi_, Jun 23 2013