C4、C5、C6成等差数列 求C12

2n!/(n-5)!5!=n!/(n-4)!4!+n!/(n-6)!6!
所以2/(n-5)!5!=1/(n-4)!4!+1/(n-6)!6!
两边乘6!*(n-4)!
2*6(n-5)=6*5+(n-5)(n-6)
12n-60=30+n^2-11n+30
n^2-23n+120=0
(n-15)(n-8)=0
要求Cn12 ,所以n不等于8
n=15
Cn12=C(15)12=15!/(15-12!)12!=15*14*13/6=455