A056948 - OEIS

%I #10 May 18 2022 21:30:38

%S 1,0,0,-2,26,0,0,32560,130812,0,0,3671562,9174424,0,0,95675472,

%T 188233758,0,0,1142977594,1959731160,0,0,8506658544,13293118872,0,0,

%U 45762829976,67073331776,0,0,195388726752,272567835540,0,0,698077270836,938806082418,0,0,2176652437872

%N Jacobi form of weight 12 and index 1 associated with a nonexistent Niemeier lattice of Coxeter number 1.

%C a(3) < 0 (apparently the only negative term) so the lattice cannot exist.

%C a(4n) + 2*Sum_{r=1..floor(sqrt(4n))} a(4*n - r^2) = A056947(n).

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

%F E_8 * E_{4, 1} + (2*h - 60) * E_{12, 1} where h = 1.

%F a(n) = A055747(n) - 58*A003785(n). - _Sean A. Irvine_, May 18 2022

%Y Cf. A003785, A055747, A056947.

%K sign

%O 0,4

%A Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 17 2000