A056947 -id:A056947 - cp's OEIS frontend

A056949 J(1)*theta3(z) where J(1) is the series given by A056948.

1, 2, 0, -2, 24, 52, 0, 32556, 195984, 261626, 0, 3736682, 16779168, 18348900, 0, 103018596, 397998672, 376729140, 0, 1334328534, 4629497040, 3937811168, 0, 10792678852, 34417510848, 26962705262, 0, 62783490188, 187489533504, 138066125924, 0, 287105737648, 814881802320

Offset: 0

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

sign

a(4n) gives the series A056948(n). It seems only a(3) is negative. What are a(4n+1), a(4n+3)?

Eichler and Zagier, The Theory of Jacobi form, Birkhauser, 1985

Cf. A056947, A056948.

(E_8*E_{4, 1}-56*E_{12, 1})*theta_3(z)

A056948 Jacobi form of weight 12 and index 1 associated with a nonexistent Niemeier lattice of Coxeter number 1.

Original entry on oeis.org

1, 0, 0, -2, 26, 0, 0, 32560, 130812, 0, 0, 3671562, 9174424, 0, 0, 95675472, 188233758, 0, 0, 1142977594, 1959731160, 0, 0, 8506658544, 13293118872, 0, 0, 45762829976, 67073331776, 0, 0, 195388726752, 272567835540, 0, 0, 698077270836, 938806082418, 0, 0, 2176652437872

Offset: 0

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

sign

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

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

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

Cf. A003785, A055747, A056947.

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

a(n) = A055747(n) - 58*A003785(n). - Sean A. Irvine, May 18 2022

cp's OEIS Frontend

A056949 J(1)*theta3(z) where J(1) is the series given by A056948.

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