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Inspired by Armin Straub's conjecture (arXiv:1601.07161) about the number andmaximal size of (2n+1, 2n+3)-core partitions with distinct parts, we developrelatively efficient, symbolic-computational algorithms, based on non-linearfunctional recurrences, to generate the generating functions, according tosize, of the set of such partitions. By computing these polynomials forn=1,...21, we are able to rigorously derive explicit expressions for theexpectation, variance, and third through seventh moments of the random variable"size of a (2n+1, 2n+3)-core partition with distinct parts." In particular, wefind that this random variable is not asymptotically normal as n goes toinfinity.

Explicit (Polynomial!) Expressions for the Expectation, Variance and  Higher Moments of the Size of a (2n + 1, 2n + 3)-core partition with Distinct  Parts