A004674 - OEIS

%I #15 Oct 26 2023 09:28:14

%S 1,0,0,2611200,19524758400,19715347537920,5615943999897600,

%T 667995073382707200,41929879624021065600,1615294860315735244800,

%U 42338358774994331566080,812656958650918956288000,12060148245903215066380800

%N Theta series of extremal even unimodular lattice in dimension 64.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 195.

%H Andy Huchala, <a href="/A004674/b004674.txt">Table of n, a(n) for n = 0..20000</a>

%F G.f.: E4(q)^8 - 1920 * E4(q)^5 * Delta(q) + 627840 * E4(q)^2 * Delta(q)^2 with E4(q) as in A004009 and Delta(q) as in A000594. - _Andy Huchala_, Jun 04 2021

%e G.f.: 1 + 2611200*q^3 + 19524758400*q^4 + ...

%o (Sage)

%o e4 = eisenstein_series_qexp(4,20,normalization = "integral");

%o delta = CuspForms(1,12).0.q_expansion(20);

%o e4^8 - 1920*e4^5*delta + 627840*e4^2*delta^2 # _Andy Huchala_, Jun 04 2021

%Y Cf. A000594, A004009.

%K nonn

%O 0,4

%A _N. J. A. Sloane_