I don't know.I thought it's true.
Recursive algrithm is true.
c++:

#include<iostream>
using namespace std;
int main()
{
    int n,k;
    cin>>n>>k;
    long long int A[11][17];
    for(int i=2;i<11;i++)
            A[0][i]=1;
    for(int i=2;i<11;i++)
            A[1][i]=i-1;
    for(int i=2;i<11;i++)
            for(int j=2;j<17;j++)
            {
                   A[i][j]=(j-1)*(A[i-1][j]+A[i-2][j]);
            }
    cout<<A[n][k];
    cin>>n;
    return 0;
}

I got Ac.Size of A was small.