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

0,2

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

Cf. A004011, A108096.

Sequence in context: A113393 A138426 A291104 * A052744 A267620 A275334

Adjacent sequences: A108089 A108090 A108091 * A108093 A108094 A108095

Keyword

sign

Author

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

Status

approved