OFFSET
0,3
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 102.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..443
FORMULA
a(0) = 1; a(n) = -(n-1)! * Sum_{k=1..n} A186690(k) * a(n-k)/(n-k)!. - Seiichi Manyama, Jul 07 2023
EXAMPLE
theta_3(q)^(-1/2) = 1 - q + 3/2 * q^2 - 5/2 * q^3 + 27/8 *q^4 - 39/8 * q^5 + ... = 1 - q + 3/2! * q^2 - 15/3! * q^3 + 81/4! * q^4 - 585/5! * q^5 + ... .
MATHEMATICA
nmax = 25; CoefficientList[Series[EllipticTheta[3, 0, x]^(-1/2), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 23 2018 *)
CROSSREFS
KEYWORD
sign
AUTHOR
STATUS
approved