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A072839 Expansion of F_9(q^2).

%I A072839 #25 Nov 11 2021 10:45:20
%S A072839 1,0,0,0,0,0,0,0,18,0,0,0,0,0,72,0,0,0,240,0,252,0,0,0,0,0,504,0,0,0,
%T A072839 0,0,1026,0,0,0,2160,0,1512,0,0,0,0,0,2664,0,0,0,0,0,3528,0,0,0,6720,
%U A072839 0,5616,0,0,0,0,0,6552,0,0,0,0,0,9828,0,0,0,17520,0,11232,0,0,0,0,0,16380,0,0
%N A072839 Expansion of F_9(q^2).
%C A072839 Theta series of {A_8}* lattice. - _Andy Huchala_, Jul 01 2021
%H A072839 G. C. Greubel, <a href="/A072839/b072839.txt">Table of n, a(n) for n = 0..1000</a>
%H A072839 S. Ahlgren, <a href="https://doi.org/10.1090/S0002-9939-99-05181-3">The sixth, eighth, ninth and tenth powers of Ramanujan's theta function</a>, Proc. Amer. Math. Soc. 128 (2000), 1333-1338.
%H A072839 K. S. Chua. <a href="https://doi.org/10.1090/S0002-9939-01-06080-4">The Root Lattice An* and Ramanujan's Circular Summation of Theta Functions</a>, Proceedings of the American Mathematical Society, 130 (2001), 1-8.
%t A072839 f[x_,y_]:= QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; CoefficientList[Series[f[q^9, q^9]^8 - 16*q^9*f[q^9, q^27]^8 + 256*q^18*f[q^18, q^54]^8 + 18*q^8*f[q^18, -q^36]^12/f[q^6, -q^12]^4, {q, 0, 100}], q] (* _G. C. Greubel_, Apr 15 2018 *)
%o A072839 (Magma)
%o A072839 L := Dual(Lattice("A", 8));
%o A072839 T<q> := ThetaSeries(L,32); Coefficients(T); // _Andy Huchala_, Jul 01 2021
%Y A072839 Cf. A008448 (dual), A072835.
%Y A072839 A023920 aerated with 0's.
%K A072839 nonn
%O A072839 0,9
%A A072839 _N. J. A. Sloane_, Jul 25 2002