@Carl Love 
Thanks for helping!

Your example is easier to understand than Wikipedia!

If I have any other questions,could I contact with you?

@Kitonum 

Thank you provide your procedure.

It's helpful to me!! :)

@Carl Love 
Thanks for your very detailed answer! I probably know how the program works, but I think that I still need some time to understand what is Ferrers diagrams.
I have a question for this syntax partition(n-k, min(n-k, k)).

Suppose that I input the number n=5 and k=2,then n-k=3.

Both of  partition(n-k, n-k) and  partition(n-k, k) don't have the error 

 EX1:  >P = combinat:-partition(5-2, 2);  #partition(n-k,k)
                    P = [[1, 1, 1], [1, 2]]

 EX2:   >P = combinat:-partition(5-2, 3);  #partition(n-k,n-k)
                    P = [[1, 1, 1], [1, 2], [3]]

( I know EX2 in the all procedure wil be wrong, and EX1 is correct.  )    

Why I always need to use min(n-k,k)?

Because the output in the EX2: [3] such that seq([0$(k-p), 1$p], p= P)  the length>k?

Use min(n-k,k)  is the rule of Ferrers diagrams,too?

@Carl Love 
Can I ask a question?
please explain this:

[seq(1 +~ `+`(seq([0$(k-p), 1$p], p= P)), P= combinat:-partition(n-k, min(n-k, k)))]

I don't understand it.   
Thank you!!

@nm 

I still thank for your answer! 

@dharr 
I know the method,but I hope the procedure can use more logical coding.
Sorry,I don't express exactly.
In short,I want a method with no package.

@Kitonum 
I have seen the procedure. Although the procedure can solve my problem,
it is too hard to to me. My problem is no other restrictions, so I think what I want to do is more simple.