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I suspect that it relates to convergence. Here are some experiments which may give a clue to that. Sum[Binomial[m - r - 1, b] z^(r + b) (-1)^(a + b + r + 1), {b, 0, m - r - 1, 1}, GenerateConditions -> True] ConditionalExpression[((-1)^(a + r) (1 - z)^(m - r) z^r)/(-1 + z), m - r \[Element] Integers && (z != 1 || Re[m - r] > 1) && m ...


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In retrospect, all the clues were thereā€¦ In order to run evolve on the parallel kernels Mathematica must first distribute the necessary definitions to those kernels, and recursively distribute the definitions involved in those definitions, all the way back. Which in my case turned out to involve way too much data (mostly a bunch of InterpolatingFunctions) ...


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Did you try DistributeDefinitions[evolve] before running ParallelTable ?



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