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Expansion of Jacobi form of weight 12 and index 1 for the Niemeier lattice of type E_8^3 or D_16+E_8.
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%I #8 Apr 05 2022 04:55:52

%S 1,0,0,56,606,0,0,27456,123156,0,0,3745512,9217112,0,0,95209152,

%T 188066718,0,0,1144371624,1960489800,0,0,8505838656,13289979912,0,0,

%U 45755357024,67080028224,0,0,195411318912,272570040468,0,0

%N Expansion of Jacobi form of weight 12 and index 1 for the Niemeier lattice of type E_8^3 or D_16+E_8.

%C a(4*n-r^2) gives number of vectors x in the lattice of norm 2n and <x,y>=r for any fixed vector in the lattice of norm 2.

%D M. Eichler and D. Zagier, The Theory of Jacobi Forms, Birkhauser, 1985.

%F E_8*E_4, 1.

%F G.f.: b(z) * c(z) where b(z) is g.f. for A003783 and c(z) = 1 + 240*z^4 + 2160*z^8 + ... is A004009 expanded in powers of z^4. - _Sean A. Irvine_, Apr 05 2022

%Y Cf. A008411, A003783, A004009.

%K nonn

%O 0,4

%A Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 11 2000