A108092 Coefficients of series whose 4th power is the theta series of D_4 (see A004011).

1, 6, -48, 672, -10686, 185472, -3398304, 64606080, -1261584768, 25141699590, -509112525600, 10443131883360, -216500232587520, 4528450460408448, -95438941858567104, 2024550297637849728, -43190698219545864702, 925997705081213764608, -19940633776083900614736, 431091393800371703940576

Offset: 0

Author

N. J. A. Sloane and Michael Somos, Jun 06 2005

Keywords

• sign

Examples

			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 + ...
		

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.

Crossrefs

Cf. A004011, A108096.

Programs

Mathematica

CoefficientList[Series[(EllipticTheta[3,0,x]^4 + EllipticTheta[2,0,x]^4)^(1/4), {x, 0, 20}], x] (* Vaclav Kotesovec, Dec 10 2017 *)

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