we are taking n=9
C(9,0)=9!/9!0!=1
C(9,1)=9!/1!8!=9
C(9,2)=9!/2!7!=36
C(9,3)=9!/3!6!=84
C(9,4)=9!/4!5!=126
C(9,5)=9!/4!5!=126
C(9,6)=9!/3!6!=84
C(9,7)=9!/2!7!=36
C(9,8)=9!/1!8!=9
C(9,9)=9!/9!0!=1
here you can see
1,9,36,84,126,126,84,36,9,1
1=C(9,0)<C(9,1)<C(9,2)<C(9,3)<C(9,4)=C(9,4)>C(9,6)>C(9,7)>C(9,8)>C(9,9)=1