0,3

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 130, p. 131 Equation (132).

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.

G. Nebe and N. J. A. Sloane, Home page for this lattice

Index entries for sequences related to Barnes-Wall lattices

Eric Weisstein's World of Mathematics, Theta Series

Eric Weisstein's World of Mathematics, Barnes-Wall Lattice

Expansion of ( theta_2(q)^16 + theta_3(q)^16 + theta_4(q)^16 + 30 * theta_2(q)^8 * theta_3(q)^8 ) / 2 in powers of q. - [Conway and Sloane]

Expansion of E_4(q^2)^2 + (E_4(q) - E_4(q^2))^2 / 15 in powers of q. - Michael Somos Nov 29 2007

Expansion of ( eta(q)^48 + 32 * eta(q)^24 * eta(q^2)^24 + 4096 * eta(q^2)^48 ) / ( eta(q) * eta(q^2) )^16 in powers of q. - Michael Somos Nov 29 2007

G.f. is Fourier series of a weight 8 level 2 modular form. f(-1 / (2 t)) = 16 (t/i)^8 f(t) where q = exp(2 pi i t). - Michael Somos Nov 29 2007

1 + 4320*q^4 + 61440*q^6 + 522720*q^8 + 2211840*q^10 + 8960640*q^12 + ...

(PARI) {a(n) = local(A1, A2) ; if( n<0, 0, A1 = eta(x + x * O(x^n))^8; A2 = eta(x^2 + x * O(x^n))^8; polcoeff( (A1^6 + 32 * x * A1^3 * A2^3 + 4096 * x^2 * A2^6) / ( A1 * A2 )^2, n))} /* Michael Somos Nov 29 2007 */

A008774(2*n) = a(n).

Sequence in context: A165067 A055153 A145312 this_sequence A028384 A107542 A145916

Adjacent sequences: A008406 A008407 A008408 this_sequence A008410 A008411 A008412

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).