A004672 - OEIS

A004672

Theta series of extremal even unimodular lattice in dimension 48.

1, 0, 0, 52416000, 39007332000, 6609020221440, 437824977408000, 15173208925056000, 327259384199748000, 4913603518247424000, 55439899840480296960, 496425571825135680000, 3672747716246756784000

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 195.

LINKS

Andy Huchala, Table of n, a(n) for n = 0..20000

N. Elkies, Rational Lattices and their Theta Functions, Equation 8, 7-8.

N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, arXiv:math/0509316 [math.NT], 2005-2006; J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

FORMULA

G.f.: E4(q)^6 - 1440 * E4(q)^3 * Delta(q) + 125280 * Delta(q)^2 with E4(q) as in A004009 and Delta(q) as in A000594.

EXAMPLE

G.f.: 1 + 52416000*q^3 + 39007332000*q^4 + ...

PROG

(Sage)

e4 = eisenstein_series_qexp(4, 20, normalization = "integral");

delta = CuspForms(1, 12).0.q_expansion(20);

e4^6-1440*e4^3 *delta+125280*delta^2 # Andy Huchala, May 09 2021

CROSSREFS

Cf. A000594, A004009.

Sequence in context: A015392 A211237 A105381 * A029824 A186596 A205180

Adjacent sequences: A004669 A004670 A004671 * A004673 A004674 A004675

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved