kappa_1..12(chi): Bernoulli derivative recursion == moment-cumulant recursion: True (kappa_2 = 1, kappa_3 = u - 1/u)
E M^0..12: power-series exponential == set partitions without singletons: True; monomial counts [1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21]
exact enumeration check (u in 12/5, 5/2, 21/10; n in 3, 5, 7; random rational beta): 351 moment identities, all exact: True
ALL PASS
