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  1. ; ; ; (, Random Structures & Algorithms)
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  2. (, The Ramanujan Journal)
    We study the Taylor expansion around the point x=1 of a classical modular form, the Jacobi theta constant θ3. This leads naturally to a new sequence (d(n)) = 1, 1, -1, 51, 849, -26199, ... of integers, which arise as the Taylor coefficients in the expansion of a related "centered" version of θ3. We prove several results about the numbers d(n) and conjecture that they satisfy the congruence d(n)≡(−1)^(n-1) (mod 5) and other similar congruence relations. 
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