Lah Numbers

The Lah number L(2, 3) is the number of ways to arrange 3 objects into 2 groups, such that the first group contains at least one object. In this case, there are 2 ways to do this: {1, 2, 3} and {1, 2}, {3}.

The Lah number L(4, 5) is the number of ways to arrange 5 objects into 4 groups, such that the first group contains at least one object. In this case, there are 20 ways to do this.

The Lah number L(6, 7) is the number of ways to arrange 7 objects into 6 groups, such that the first group contains at least one object. In this case, there are 70 ways to do this.

The Lah number L(8, 9) is the number of ways to arrange 9 objects into 8 groups, such that the first group contains at least one object. In this case, there are 126 ways to do this.

The Lah number L(10, 11) is the number of ways to arrange 11 objects into 10 groups, such that the first group contains at least one object. In this case, there are 220 ways to do this.

The Lah number L(12, 13) is the number of ways to arrange 13 objects into 12 groups, such that the first group contains at least one object. In this case, there are 342 ways to do this.

The Lah number L(14, 15) is the number of ways to arrange 15 objects into 14 groups, such that the first group contains at least one object. In this case, there are 512 ways to do this.

The Lah number L(16, 17) is the number of ways to arrange 17 objects into 16 groups, such that the first group contains at least one object. In this case, there are 748 ways to do this.

The Lah number L(18, 19) is the number of ways to arrange 19 objects into 18 groups, such that the first group contains at least one object. In this case, there are 1024 ways to do this.

The Lah number L(20, 21) is the number of ways to arrange 21 objects into 20 groups, such that the first group contains at least one object. In this case, there are 1331 ways to do this.

The Lah number L(22, 23) is the number of ways to arrange 23 objects into 22 groups, such that the first group contains at least one object. In this case, there are 1683 ways to do this.

The Lah number L(24, 25) is the number of ways to arrange 25 objects into 24 groups, such that the first group contains at least one object. In this case, there are 2067 ways to do this.

The Lah number L(26, 27) is the number of ways to arrange 27 objects into 26 groups, such that the first group contains at least one object. In this case, there are 2485 ways to do this.

The Lah number L(28, 29) is the number of ways to arrange 29 objects into 28 groups, such that the first group contains at least one object. In this case, there are 2925 ways to do this.

The Lah number L(30, 31) is the number of ways to arrange 31 objects into 30 groups, such that the first group contains at least one object. In this case, there are 3403 ways to do this.