OFFSET
0,2
REFERENCES
N. J. A. Sloane, Seven Staggering Sequences, in Homage to a Pied Puzzler, E. Pegg Jr., A. H. Schoen and T. Rodgers (editors), A. K. Peters, Wellesley, MA, 2009, pp. 93-110.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..730
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.
N. J. A. Sloane, Seven Staggering Sequences.
N. J. A. Sloane, Old and New Problems from 55 Years of the OEIS, Slides of talk in Doron Zeilberger's Experimental Math Seminar at Rutgers University, October 10 2019.
FORMULA
a(n) ~ -(-1)^n * Gamma(1/4)^3 * exp(Pi*n) / (2^(15/4) * Pi^(5/2) * n^(5/4)). - Vaclav Kotesovec, Dec 10 2017
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 its 4th root is 1 + 6*q^2 - 48*q^4 + 672*q^6 - 10686*q^8 + 185472*q^10 - 3398304*q^12 + ...
MATHEMATICA
CoefficientList[Series[(EllipticTheta[3, 0, x]^4 + EllipticTheta[2, 0, x]^4)^(1/4), {x, 0, 20}], x] (* Vaclav Kotesovec, Dec 10 2017 *)
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane and Michael Somos, Jun 06 2005
STATUS
approved