OFFSET
0,2
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p 102 eq 9.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
FORMULA
Expansion of eta(q^2)^3 * eta(q^4) * eta(q^8) * eta(q^16) * eta(q^32)^3 / (eta(q)^2 * eta(q^64)^2) in powers of q.
EXAMPLE
G.f. = 1 + 2*x + 2*x^2 + 4*x^3 + 4*x^4 + 4*x^5 + 8*x^6 + 8*x^7 + 8*x^8 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, x] EllipticTheta[ 3, 0, x^2] EllipticTheta[ 3, 0, x^4] EllipticTheta[ 3, 0, x^8] EllipticTheta[ 3, 0, x^16], {x, 0, n}]; (* Michael Somos, Feb 22 2015 *)
PROG
(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=0, 4, sum(i=1, sqrtint( n\(2^k)), 2 * x^(2^k * i^2), 1 + x*O(x^n))), n))};
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(X)^-2 * eta(x^2 + A)^3 * eta(x^4 + A) * eta(x^8 + A) * eta(x^16 + A) * eta(x^32 + A)^3 * eta(x^64 + A)^-2, n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved