cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A056946 Coefficients of J(0)*theta_3(z) where J(0) is sequence A056945.

Original entry on oeis.org

1, 2, 0, -4, 0, 12, 0, 32728, 196560, 262154, 0, 3734484, 16773120, 18345916, 0, 103029576, 398034000, 376741188, 0, 1334312620, 4629381120, 3937755904, 0, 10792611336, 34417656000, 26962933262, 0, 62783799320, 187489935360, 138065611740, 0, 287105506144, 814879774800
Offset: 0

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Author

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

Keywords

Comments

Note a(4n)=A008408(n) gives theta series of Leech lattice. a(4n+2)=0. a(3)<0, apparently the only negative term. What are a(4n+1), a(4n+3)?

References

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

Crossrefs

Cf. A008408, A056945.

Formula

(E_8*E_{4, 1}-60*E_{12, 1})*theta_3(z)

A056950 Jacobi form of weight 12 and index 1 associated with a nonexistent Niemeier lattice of Coxeter number 11.

Original entry on oeis.org

1, 0, 0, 18, 226, 0, 0, 30800, 128172, 0, 0, 3697062, 9189144, 0, 0, 95514672, 188176158, 0, 0, 1143458294, 1959992760, 0, 0, 8506375824, 13292036472, 0, 0, 45760253096, 67075640896, 0, 0, 195396517152, 272568595860, 0, 0
Offset: 0

Views

Author

Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 18 2000

Keywords

Comments

a(n)>=0, for n<1000.

References

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

Crossrefs

Cf. A003785, A055747, A056945.

Formula

E_8 * E_{4, 1} + (2*h - 60) * E_{12, 1} where h = 11.
a(n) = A055747(n) - 38*A003785(n). - Sean A. Irvine, May 18 2022
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