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Recently, Romik determined in [9] the Taylor expansion of the Jacobi thetaconstant \theta_3, around the point x = 1. He discovered a new integersequence, (d(n))_0^\infty=1, 1, -1, 51, 849, -26199, \dots, from which theTaylor coefficients are built, and conjectured that the numbers d(n) satisfycertain congruences modulo various primes. In this paper, we prove some ofthese conjectures, for example that d(n)\equiv (-1)^{n+1}(mod 5) for all n\geq1,and that for any prime p\equiv 3 (mod 4), d(n) vanishes modulo p for alllarge enough n.

Congruences modulo primes of the Romik sequence related to the Taylor expansion of the Jacobi theta constant {\theta}_3