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Expansion of (1+x^2)/((1-x)^2*(1-x^2)^2*(1-x^3)^2*(1-x^8)*(1-x^9)*(1-x^10)).
1

%I #13 Aug 16 2022 10:43:38

%S 1,2,6,12,23,40,67,104,160,235,340,480,669,913,1235,1643,2165,2818,

%T 3638,4646,5895,7413,9264,11493,14179,17377,21194,25700,31023,37263,

%U 44575,53080,62978,74417,87633,102822,120264,140193,162958,188839

%N Expansion of (1+x^2)/((1-x)^2*(1-x^2)^2*(1-x^3)^2*(1-x^8)*(1-x^9)*(1-x^10)).

%H G. C. Greubel, <a href="/A069956/b069956.txt">Table of n, a(n) for n = 0..1000</a>

%H G. E. Andrews, P. Paule and A. Riese, <a href="http://dx.doi.org/10.1006/aama.2001.0733">MacMahon's Partition Analysis VIII: Plane partition diamonds</a>, Advances Applied Math., 27 (2001), 231-242.

%H <a href="/index/Rec#order_37">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-4,-5,4,11,-4,-13,1,12,0,-9,5,6,-11,-9,15,14, -14,-15,9,11,-6,-5,9,0,-12,-1,13,4,-11,-4,5,4,-2,-2,1).

%t CoefficientList[Series[(1+x^2)/((1-x)^2(1-x^2)^2(1-x^3)^2 (1-x^8) (1-x^9)*(1-x^10)), {x,0,50}],x] (* _Harvey P. Dale_, Apr 16 2011 *)

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+x^2)/((1-x)^2(1-x^2)^2(1-x^3)^2 (1-x^8) (1-x^9)*(1-x^10)) )); // _G. C. Greubel_, Aug 16 2022

%o (SageMath)

%o def A069956_list(prec):

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

%o return P( (1+x^2)/((1-x)^2(1-x^2)^2(1-x^3)^2 (1-x^8) (1-x^9)*(1-x^10)) ).list()

%o A069956_list(50) # _G. C. Greubel_, Aug 16 2022

%K nonn

%O 0,2

%A _N. J. A. Sloane_, May 05 2002