Groovy 67, 65
(p={c,r->println' '*(109-r)+(c*(r*2-1))})'*',1;(1..109).each{p'0',it}
Surprisingly, the tree looks like this:
*
0
000
00000
0000000
000000000
00000000000
0000000000000
000000000000000
00000000000000000
0000000000000000000