# Generating permutations of coefficients

I have created the following function to return all pairs `(n, k)`

such that a slightly altered binomial coefficient is less than or equal to a certain `N`

:

```
bin = lambda n, k : binomial(n + k - 1, k)
def nkfilter(N):
pairs = []
for n in range(2, N+1):
for k in range(1, n):
if bin(n, k) <= N:
pairs.append([n, k])
print '\n (n, k)\n'
return pairs
```

This prints out the following:

```
example = nkfilter(8); print example
(n, k)
[[2, 1], [3, 1], [3, 2], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1]]
```

I now would like to take this `n`

and generate a tuple of length `n`

: `(a_1,..., a_n)`

, for which all the `a_i`

s are less than or equal to `k`

. I have been considering `permutations`

to accomplish this, but I believe I need to first generate `list_of_numbers_less_than_k`

and then take `permutations(n, list_of_numbers)`

.

However I am not sure which data types to use, and how to generate these `n`

-length tuples.