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%I #22 May 01 2021 07:33:32
%S 1,0,0,0,9694080,0,89754255360,10164979630080,639876527832960,
%T 24647440237854720,646038471835975680,12399979575839293440,
%U 184026095698230213120,2200347840694273966080,21889196776341251850240,185813171532073386639360,1373979253438910041038720
%N Theta series of Barnes-Wall lattice in 64 dimensions.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag.
%H Andy Huchala, <a href="/A103936/b103936.txt">Table of n, a(n) for n = 0..20000</a>
%H <a href="/index/Ba#BW">Index entries for sequences related to Barnes-Wall lattices</a>
%e 1 + 9694080*q^8 + 89754255360*q^12 + 10164979630080*q^14 + 639876527832960*q^16 + 24647440237854720*q^18 + 646038471835975680*q^20 + 12399979575839293440*q^22 + 184026095698230213120*q^24 + 2200347840694273966080*q^26 + ...
%e In terms of H1 = theta_{D4} and H2 = (eta(q) eta(q^2))^8: H1^16 - 384*H1^12*H2 + 38016*H1^8*H2^2 - 743424*H1^4*H2^3 + 9732096*H2^4.
%o (Sage)
%o from sage.modular.etaproducts import qexp_eta; bound = 20;
%o eta(q) = qexp_eta(ZZ[['q']], bound);
%o R.<q> = ZZ[];
%o H1 = ModularForms( Gamma0(2), 2, prec=bound).0;
%o H1 = R(H1.q_expansion());
%o H2 = R(q*(eta(q)*eta(q^2))^8);
%o f = H1^16-384*H1^12*H2+38016*H1^8*H2^2-743424*H1^4*H2^3+9732096*H2^4;
%o list(f)[:bound] # _Andy Huchala_, May 01 2021
%K nonn
%O 0,5
%A Eric Rains and _N. J. A. Sloane_, Sep 27 2005
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