How many ways can you write the natural number n as the sum of m natural numbers, in no particular order?

By recursive calculation (there is no simple formula):

Let A(n, m) be a natural number, and n is written as the sum of m natural numbers. Then:

A(n，m) = A(n- 1，m- 1) + A(n-m，m)

The meaning of this recursive formula is as follows:

We will write n as the sum of m numbers. There are two cases: (1) and the minimum number in the formula is1; (2) The minimum number in the summation formula is at least 2.

In the first case, we remove one of 1 from the summation formula, and the remaining summation formula is to write n- 1 as the sum of the numbers m- 1, so it is A(n- 1, m- 1).

In the second case, we subtract 1 from every element in the sum formula, and it becomes the sum formula of the number of m written by n-m, so it is A(n-m, m).

The rest is the initial value:

For any n, a (n, 1) = a (n, n) =1;

According to the recursive calculation method, step by step, is possible.

In fact, it is to fill in the form of A(i, J), column by column.