The On-Line Encyclopedia of Integer Sequences (OEIS)

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A056946

Coefficients of J(0)*theta_3(z) where J(0) is sequence A056945.
(history; published version)

#3 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

FORMULA

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

KEYWORD

sign,new

sign

#2 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

REFERENCES

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

KEYWORD

sign,new

sign

AUTHOR

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

#1 by N. J. A. Sloane at Sat Jul 22 03:00:00 EDT 2000

NAME

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

DATA

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

0,2

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 & Zagier, The Theory of Jacobi forms, Birkhauser, 1985.

FORMULA

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

CROSSREFS

Cf. A008408, A056945.

KEYWORD

sign

AUTHOR

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

STATUS

approved