Suppose with . Then find the number of ways in which with and for all
You do realize that the partition function P(n), the number of ways a natural number n can be partitioned as the sum of smaller numbers, is given by Hardy and Ramanujan's complicated formula:
where
Are you attempting to place an upper limit on the highest addend in effort to simplify this formula? Or do you seek an algorithmic solution?
Thanks for your reply.
In P(d) there is no restriction on the number of .
But in my question each partition of must have exactly values (including repetitions) and all those partitioned values ( ) must be .
Is there any formula for such a case ?