A(n+1,m)-A(n,m)
=(n+1)!/(n-m+1)!-n!/(n-m)!
=[(n+1)!-n!(n-m+1)]/(n-m+1)!
=n![(n+1)-(n-m+1)]/(n-m+1)!
=n!*m/(n-m+1)!
=mA(n,m-1)
A(n+1,m)-A(n,m)
=(n+1)!/(n-m+1)!-n!/(n-m)!
=[(n+1)!-n!(n-m+1)]/(n-m+1)!
=n![(n+1)-(n-m+1)]/(n-m+1)!
=n!*m/(n-m+1)!
=mA(n,m-1)