Binomial Coefficients and Generating Functions - Cs.ioc.ee

Vandermonde’s identity (2)
Equating coefficients of z k on both sides of this equation gives:
Convolution yields
1
1
1 9
1
8
1
7
1
6
28
1
5
21
36 84
1
4
15
56
1
3
10
35
1
2
6
20
70
Vandermonde’s convolution:
k
m n m + n
∑
=
j=0 j k − j k
1
3
10
35
126 126
1
4
15
56
1
5
21
1
6
28
1
7
84 36
1
8
1
1
9 1
9 3 6 3 6 3 6
= + +
2 0 2 1 1 2 0