Math, Statistics &amp; Probability

Exact Derangement Number Calculator

Count exact no-fixed-point permutations with the subfactorial recurrence.

Exact Harmonic Number Calculator

Calculate a finite harmonic number as an exact reduced fraction and decimal.

Exact Integer Bell Number Calculator

Count partitions of labelled elements into any number of nonempty unlabeled blocks.

Exact Integer Catalan Number Calculator

Calculate a bounded exact Catalan sequence term with a multiplicative recurrence.

Exact Jacobsthal Number Calculator

Calculate a Jacobsthal term with the doubled two-back recurrence.

Exact Lah Number Calculator

Count partitions of labelled elements into internally ordered nonempty blocks.

Exact Lucas Number Calculator

Calculate a bounded exact Lucas sequence term from its defining recurrence.

Exact Motzkin Number Calculator

Count nonnegative level-step lattice paths of an exact bounded length.

Exact Narayana Number Calculator

Count Dyck paths of a bounded semilength with an exact number of peaks.

Exact Padovan Number Calculator

Calculate a Padovan term under the explicit zero-based 1,1,1 convention.

Exact Part Integer Partition Calculator

Count unordered partitions of n containing exactly k positive parts.

Exact Pell Sequence Calculator

Calculate a Pell sequence term from its zero-one coefficient-two recurrence.