A317651 Sequence related to the Taylor expansion of the Jacobi theta_3 constant.

1, 1, -1, 51, 849, -26199, 1341999, 82018251, 18703396449, -993278479599, -78795859032801, 38711746282537251, -923351332174412751, 4688204953344642495801, 501271295036889289819599, -89944302490128540556106949, -104694993963067299023875442751, 63396004159664562363095882996001

Offset: 0

Author

Michel Marcus, Aug 03 2018

Keywords

• sign

Links

• Christian Krattenthaler and Thomas W. Müller, The congruence properties of Romik's sequence of Taylor.coefficients of Jacobi's theta function theta_3, arXiv:2304.11471 [math.NT], 2023. See p. 1.
• Dan Romik, The Taylor coefficients of the Jacobi theta_3, arXiv:1807.06130 [math.NT], 2018.
• Robert Scherer, Congruences modulo primes of the Romik sequence related to the Taylor expansion of the Jacobi theta constant theta_3, arXiv:1904.04509 [math.NT], 2019.
• Tanay Wakhare, Christophe Vignat, Taylor coefficients of the Jacobi theta3(q) function, arXiv:1909.01508 [math.NT], 2019.

Crossrefs

Cf. A175573 (theta3(1)).

Extensions

More terms from Romik article added by Michel Marcus, Apr 10 2019