Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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