A108093 Coefficients of series whose 24th power is the theta series of the Leech lattice (see A008408).

1, 0, 8190, 698880, -754790400, -131455134720, 90235527782400, 25034722952279040, -11631379080860106750, -4740180695347850188800, 1500620323887236434821120, 888527739621938585682240000, -181995668700704689414022799360, -164466129435036361896228722795520

Offset

0,3

References

N. J. A. Sloane, Seven Staggering Sequences, in Homage to a Pied Puzzler, E. Pegg Jr., A. H. Schoen and T. Rodgers (editors), A. K. Peters, Wellesley, MA, 2009, pp. 93-110.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..378

N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

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.

N. J. A. Sloane, Seven Staggering Sequences.

Eric Weisstein's World of Mathematics, Leech Lattice

Example

More precisely, the theta series of the Leech lattice (A008408) begins 1 + 196560*q^4 + 16773120*q^6 + 398034000*q^8 + 4629381120*q^10 + ... and the 24th root of this is 1 + 8190*q^4 + 698880*q^6 - 754790400*q^8 - 131455134720*q^10 + ...

Mathematica

terms = 14; s = (-45/16 EllipticTheta[2, 0, q]^8 EllipticTheta[3, 0, q]^8 EllipticTheta[4, 0, q]^8 + 1/8 (EllipticTheta[2, 0, q]^8 + EllipticTheta[3, 0, q]^8 + EllipticTheta[4, 0, q]^8)^3)^(1/24) + O[q]^(2 terms); (* Jean-François Alcover, Jul 07 2017, from LatticeData(Leech) *)

Crossrefs

Cf. A008408.

Sequence in context: A283954 A250939 A137385 * A051334 A145592 A172315

Adjacent sequences: A108090 A108091 A108092 * A108094 A108095 A108096

Keyword

sign

Author

N. J. A. Sloane and Michael Somos, Jun 06 2005

Status

approved