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 |