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A004673 Theta series of extremal even unimodular lattice in dimension 56. 2
1, 0, 0, 15590400, 36957286800, 15284192071680, 2099603881267200, 134803322124134400, 4960017097962973200, 119289241340847513600, 2051414989573311774720, 26894038407511734144000, 281804009505443595441600 (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
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
Sequence in context: A121840 A345618 A346335 * A290385 A058909 A179585
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified February 21 13:52 EST 2024. Contains 370235 sequences. (Running on oeis4.)