Ruby: 51 characters

p=[];$_.to_i.times{n=0;p p.map!{|i|v=n;n=i;v+i}<<1}

Sample run:

bash-4.2$ ruby -ne 'p=[];$_.to_i.times{n=0;p p.map!{|i|v=n+i;n=i;v}<<1}' <<< 1
[1]

bash-4.2$ ruby -ne 'p=[];$_.to_i.times{n=0;p p.map!{|i|v=n+i;n=i;v}<<1}' <<< 9
[1]
[1, 1]
[1, 2, 1]
[1, 3, 3, 1]
[1, 4, 6, 4, 1]
[1, 5, 10, 10, 5, 1]
[1, 6, 15, 20, 15, 6, 1]
[1, 7, 21, 35, 35, 21, 7, 1]
[1, 8, 28, 56, 70, 56, 28, 8, 1]