Consider $P(n)$ as a number of $n$-permutations, which each cycle have even length, and ...
114752
Number of permutations of a specific cycle decomposition
70620
From $n=2$ to $n$-ary Euclid lemma $\ p\mid a_1\cdots a_n\Rightarrow\ p\mid a_1\,$ or $\,\cdots\, p\mid a_n$
33216
Prove that the order of an element in $S_n$ equals the least common multiple of the lengths of the cycles in its cycle decomposition.
13771
Why are two permutations conjugate iff they have the same cycle structure?
83837
Odd/Even Permutations
105911
The number of permutations of $\{1,2,\ldots,n\}$ that have exactly one ascent (rise).
41008
how many permutations of {1,2,...,9}
30003
Proving that Order for N is Anti-symmetric
99634
$\binom{n}{1},\binom{n}{2},\ldots ,\binom{n}{n-1}$ are all even numbers.
37012
The number of summands $\phi(n)$
134440
An unexpected application of non-trivial combinatorics
108747
A simple permutation question - discrete math
123567
Number of permutations which are products of exactly two disjoint cycles.
92554
How many lattice paths are there from $(0,0)$ to $(2n,2n)$ that avoids odd points
128834
Proving the number of even and odd permutations of a subgroup $H<S_{n}$ are equal, provided $H$ is not contained in $A_{n}$
104549
When $d \mid n$, the number of elements of order $d$ in a cyclic subgroup of order $n$ is $\phi (d)$
93459
Number of permutations of unspecified length