0,2

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.

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).

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.

# Extremal theta series:

read(`/usr/njas/bin/format`); kernelopts(printbytes=false): interface(screenwidth=200); with(numtheory);

# set mu:

for mu from 1 to 100 do

# set max deg:

md:=mu+3;

f:=1+240*add(sigma[3](i)*x^i, i=1..md);

f:=series(f, x, md);

f:=series(f^3, x, md);

g:=series(x*mul( (1-x^i)^24, i=1..md), x, md);

W0:=series(f^mu, x, md):

h:=series(g/f, x, md):

A:=series(W0, x, md):

Z:=A:

for i from 1 to mu do

Z:=series(Z*h, x, md);

A:=series(A-coeff(A, x, i)*Z, x, md);

od:

lprint(A);

od:

Cf. A034598 (second coefficient, which eventually becomes negative), A034414, A034415.

Adjacent sequences: A034594 A034595 A034596 this_sequence A034598 A034599 A034600

Sequence in context: A074388 A008408 A001942 this_sequence A037148 A024211 A113919

nonn

njas