# What does the Combinatorica function: NumberOfPermutationsByType return?

I am using Mathematica 9. If I input:

NumberOfPermutationsByType[{2, 2, 1, 1}]


Mathematica returns 1/8. I was expecting 45, the number of permutations of {1,2,3,4,5,6} with cycle lengths 2,2,1,1.

The type of a permutation of length $n$ is $\{\lambda_1, \lambda_2, \ldots, \lambda_n\}$ where $\lambda_i$ is the number of cycles of length $i$. Therefore, the number of permutations of $\{1, 2, 3, 4, 5, 6\}$ that have two 1-cycles and two 2-cycles is
NumberOfPermutationsByType[{2, 2, 0, 0, 0, 0}]

NumberOfPermutationsByType[l_List] :=