{n\brack k}

Stirling numbers of the first kind, denoted as {n\brack k}, count the number of permutations of n elements with exactly k permutation cycles. They are used in combinatorics to study permutations and their properties.

Examples

The number of permutations of 5 elements with exactly 2 cycles.

{5\brack 2} = 50

The number of permutations of 4 elements with exactly 1 cycle.

{4\brack 1} = 6

The number of permutations of 6 elements with exactly 3 cycles.

{6\brack 3} = 90