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A034598 Second coefficient of extremal theta series of even unimodular lattice in dimension 24n. 4
1, 16773120, 39007332000, 15281788354560, 2972108280960000, 406954241261568000, 45569082381053868000, 4499117081888292864000, 408472720963469499617280, 34975479259332252426240000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Although these initially increase, they eventually go negative at about term 1700 (i.e. dimension about 40800) - see references.

REFERENCES

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

C. L. Mallows, A. M. Odlyzko and N. J. A. Sloane, "Upper bounds for modular forms, lattices and codes", J. Alg., 36 (1975), 68-76.

C. L. Mallows and N. J. A. Sloane, An Upper Bound for Self-Dual Codes, Information and Control, 22 (1973), 188-200.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..100

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (Abstract, pdf, ps).

N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).

EXAMPLE

When n=1 we get the theta series of the 24-dimensional Leech lattice: 1+196560*q^4+16773120*q^6+... (see A008408). For n=2 we get A004672 and for n=3, A004675.

MAPLE

For Maple program see A034597.

CROSSREFS

Cf. A034597 (leading coefficient).

Sequence in context: A248204 A178555 A255164 * A011574 A022540 A223604

Adjacent sequences:  A034595 A034596 A034597 * A034599 A034600 A034601

KEYWORD

sign

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 28 21:25 EDT 2017. Contains 284246 sequences.