P 1 * := 1

P 2 k :=
    f 1 := 1
    f 2 := 2
    f n := + (f - n 1) (f - n 2)
    return f k

P 3 k :=
    f 1 := 1
    f 2 := 3
    f n := + (f - n 1) * 2 (f - n 2)
    return f k

P 4 k :=
    J 1 := 1
    J 2 := 2
    J n := + (J - n 1) (P 4 - n 1)
    f 1 := 1
    f 2 := 5
    f n := + + (P 4 - n 1) * 4 (f - n 2) * 2 (J - n 2)
    return f k