Integer Partition

In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. If order matters, the sum becomes a composition. For example, 4 can be partitioned in five distinct ways:
    4
3 + 1
2 + 2
2 + 1 + 1
1 + 1 + 1 + 1
exp_sum(1) # 1
exp_sum(2) # 2  -> 1+1 , 2
exp_sum(3) # 3 -> 1+1+1, 1+2, 3
exp_sum(4) # 5 -> 1+1+1+1, 1+1+2, 1+3, 2+2, 4
exp_sum(5) # 7 -> 1+1+1+1+1, 1+1+1+2, 1+1+3, 1+2+2, 1+4, 5, 2+3

exp_sum(10) # 42
exp_sum(50) # 204226
exp_sum(80) # 15796476
exp_sum(100) # 190569292
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@solution:

import operator
get_last_item = operator.itemgetter(-1)
def exp_sum(n):
    p_matrix=[[0]*(n+1) for x in range(n+1)]
    # return p_matrix
    for i in range(0,n+1):
        p_matrix[i][0]=1
    for i in range(1,n+1):
        for j in range(1,n+1):
            if i>j:
                p_matrix[i][j]=p_matrix[i-1][j]
            else:
                exclude_i=p_matrix[i-1][j]
                include_i=p_matrix[i][j-i]
                p_matrix[i][j]=exclude_i+include_i
    return p_matrix[n][-1]