human
I found an interesting problem on https://www.codewars.com/kata/52ec24228a515e620b0005ef:
# How many ways can you make the sum of a number?

From wikipedia: https://en.wikipedia.org/wiki/Partition_(number_theory)#

>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
```

## Examples

### Basic

```python
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
```

### Explosive

```python
exp_sum(50) # 204226
exp_sum(80) # 15796476
exp_sum(100) # 190569292
```

See [here](http://www.numericana.com/data/partition.htm) for more examples.

I tried it in Python, but could not do it. Can you solve it?
assistant
#Here is the Python code you requested.

class Memoize:
    def __init__(self, func): 
        self.func = func
        self.cache = {}
    def __call__(self, arg):
        if arg not in self.cache: 
            self.cache[arg] = self.func(arg)
        return self.cache[arg]

@Memoize
def exp_sum(n):
    if n == 0: return 1
    result = 0; k = 1; sign = 1; 
    while True:
        pent = (3*k**2 - k) // 2        
        if pent > n: break
        result += sign * exp_sum(n - pent) 
        pent += k
        if pent > n: break
        result += sign * exp_sum(n - pent) 
        k += 1; sign = -sign; 
    return result