Use this exact counting tool when the selection order, repetition rule, and integer domain are unambiguous.

n

Required integer input.

Compute the nth Catalan number using the multiplicative formula. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Catalan number

The resulting catalan number returned as an integer.

• Combinatorial counts grow rapidly and may exceed practical enumeration or supported integer ranges. Similar-looking formulas answer different questions when order or repetition changes.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

State whether order matters and whether repetition is allowed before selecting a formula. For large results, use arbitrary-precision arithmetic or logarithms and avoid generating every arrangement unnecessarily.

• Combination Count Calculator

  Calculate the number of unordered ways to choose k items from n items.

• Permutation Count Calculator

  Calculate the number of ordered ways to choose k items from n items.

• Double Factorial Calculator

  Calculate the double factorial of a nonnegative integer.