@vv 
Thank you for this elegant solution. I have tried it and it works well.

Actually, I think this should be added to the Maple documentation, if not already there. I could not find it, but now I am happy to have it. Thank you.

@Kitonum 

Thank you for the reply. This works for small numbers like 15,8 but not for the larger ones, as Maple takes too long. I started this last night:

combinat:-partition(100,35): 

myt := select(t->nops(t)=nops({t[]}), %);

numelems(myt);

and it is still running after eleven hours!, while the SageMath code above only took about five minutes!

Is there another way of just getting the count, not the whole list?