A004673 Theta series of extremal even unimodular lattice in dimension 56.

1, 0, 0, 15590400, 36957286800, 15284192071680, 2099603881267200, 134803322124134400, 4960017097962973200, 119289241340847513600, 2051414989573311774720, 26894038407511734144000, 281804009505443595441600

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. 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

E4^7 - 1680 * E4^4 * Delta + 347760 * E4 * Delta^2 with E4(q) as in A004009 and Delta(q) as in A000594. - Andy Huchala, Jun 05 2021

Example

G.f.: 1 + 15590400*q^3 + 36957286800*q^4 + ...

Prog

(Sage)
e4 = eisenstein_series_qexp(4, 20, normalization = "integral");
delta = CuspForms(1, 12).0.q_expansion(20);
e4^7 - 1680*e4^4*delta + 347760*e4*delta^2 # Andy Huchala, Jun 05 2021

Crossrefs

Cf. A000594, A004009.

Sequence in context: A121840 A345618 A346335 * A290385 A058909 A179585

Adjacent sequences: A004670 A004671 A004672 * A004674 A004675 A004676

Keyword

nonn

Author

N. J. A. Sloane

Status

approved