由于

C

n+1n+3

=

C

n-1n+1

+

C

nn+1

+

C

n-2n

，

则

C

2n+3

=

C

2n+1

+

C

1n+1

+

C

2n

即

(n+3)(n+2)

2

=

(n+1)n

2

+(n+1)+

n(n-1)

2

，

整理得n²-3n-4=0

又由n∈N^*，则n=4，则

A

nn

=

A

44

=4!=24．