# Lah numbers

Use this tool to calculate Lah numbers and find below a table of some Lah numbers.

## Lah numbers formula

Assume that n and k are 2 positive integers such as $$k <= n$$ then the Lah number n, k is defined as :

$$L (n, k) =\dbinom {n-1} {k-1}\dfrac {n!}{k!}$$

$$\dbinom {n} {k}$$ refers to binomial coefficient ('n choose k').

## Lah Numbers Table

n \ k 1 2 3 4 5 6 7 8 9 10
1 1
2 2 1
3 6 6 1
4 24 36 12 1
5 120 240 120 20 1
6 720 1800 1200 300 30 1
7 5040 15120 12600 4200 630 42 1
8 40320 141120 141120 58800 11760 1176 56 1
9 362880 1451520 1693440 846720 211680 28224 2016 72 1
10 3628800 16329600 21772800 12700800 3810240 635040 60480 3240 90 1