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Count exact no-fixed-point permutations with the subfactorial recurrence.
Calculate a finite harmonic number as an exact reduced fraction and decimal.
Count partitions of labelled elements into any number of nonempty unlabeled blocks.
Calculate a bounded exact Catalan sequence term with a multiplicative recurrence.
Calculate a Jacobsthal term with the doubled two-back recurrence.
Count partitions of labelled elements into internally ordered nonempty blocks.
Calculate a bounded exact Lucas sequence term from its defining recurrence.
Count nonnegative level-step lattice paths of an exact bounded length.
Count Dyck paths of a bounded semilength with an exact number of peaks.
Calculate a Padovan term under the explicit zero-based 1,1,1 convention.
Count unordered partitions of n containing exactly k positive parts.