is there any formula that describes the frequency distribution of numbers(from 1 to N) across all partitions of N?

Question

I was interested in frequency of numbers across all partitions of a particular number N.

say 5 = 5, 4+1, 3+2, 3+1+1, 2+2+1, 2+1+1+1, 1+1+1+1+1

frequencies of 1 to 5 are 11,3,2,1,1 respectively.

is there any formula describing their frequency distribution?

the plot of such a frequency distribution for 50 and 70 are

frequency of numbers across all partitions of 50

frequency of numbers across all partitions of 70