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Consider the following function:

def f(n) :
    def retfunc(x) : 
        return 1 if n == 0 else x*add(f(n-k) for k in (1..n))
    return retfunc

The test

w = f(9); print w, type(w)

gives

"function retfunc at 0x43d3de8" "type 'function'" 

which looks fine to me. However an evaluation w(3) gives

TypeError: unsupported operand type(s) for +: 'int' and 'function'

How can I get around this error?

Consider the following function:

def f(n) :
    def retfunc(x) : 
        return 1 if n == 0 else x*add(f(n-k) for k in (1..n))
    return retfunc

The test

w = f(9); print w, type(w)

gives

"function retfunc at 0x43d3de8" "type 'function'" 

which looks fine to me. However an evaluation w(3) gives

TypeError: unsupported operand type(s) for +: 'int' and 'function'

How can I get around this error?

def f(n):
    retfunc(x) = 1 if n == 0 else add(x*f(n-k) for k in (1..n))
    return retfunc

for i in [1..8] : [c[0] for c in expand(f(i)(x)).coeffs()]
[1]
[1, 1]
[1, 2, 1]
[1, 3, 3, 1]
[1, 4, 6, 4, 1]
[1, 5, 10, 10, 5, 1]
[1, 6, 15, 20, 15, 6, 1]
[1, 7, 21, 35, 35, 21, 7, 1]