OFFSET
0,2
COMMENTS
Do these coefficients have a number-theoretic interpretation?
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..735
N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, arXiv:math/0509316 [math.NT], 2005-2006; J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
FORMULA
a(n) ~ -(-1)^n * Gamma(1/4)^4 * exp(Pi*n) / (2^(7/2) * Pi^(7/2) * n^(3/2)). - Vaclav Kotesovec, Dec 10 2017
Convolution 4th power of this sequence gives A008658. - Georg Fischer, Mar 30 2023
EXAMPLE
More precisely, the theta series of D_4 begins 1 + 24*q^2 + 24*q^4 + 96*q^6 + 24*q^8 + 144*q^10 + 96*q^12 + ... and the square root of this is 1 + 12*q^2 - 60*q^4 + 768*q^6 - 11004*q^8 + 178200*q^10 - 3093504*q^12 + ...
MATHEMATICA
CoefficientList[Series[Sqrt[EllipticTheta[3, 0, x]^4 + EllipticTheta[2, 0, x]^4], {x, 0, 20}], x] (* Vaclav Kotesovec, Dec 10 2017 *)
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane and Michael Somos, Jun 07 2005
STATUS
approved