let me show U, fn=(n+1)!/2. I'm right,MM is...

Let 1,2,3......,n , i>1+2+......(i-1)

n=1,f1=1, n=2, 23-,32-,3-2, why don't use 1? Cs 1 can put anywhere.

n=3,f3=12    123-,213-,231-,23-1,   132-,312,321-,32-1,   13-2,31-2,3-12,3-21.

We have f(n)=(n+1)!/2 by induction, n=1,2,3 right. n=k right,see n=k+1.

fk=(k+1)!/2, one of permutaions is p1p2p3....pi-p(i+1)...pk.

1 can put in k+2 positions, so we have f(k+1)=(k+2)!/2. We got it.