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