%I
%S 1,0,1,0,1,2,0,0,4,5,0,0,2,15,14,0,0,0,15,56,42,0,0,0,5,84,210,132,0,
%T 0,0,0,56,420,792,429,0,0,0,0,14,420,1980,3003,1430,0,0,0,0,0,210,
%U 2640,9009,11440,4862,0,0,0,0,0,42,1980,15015,40040,43758,16796,0,0,0,0,0,0
%N Expansion of c(x*y(1+x)), c(x) the g.f. of A000108.
%C Row sums are A052709(n+1). Diagonal sums are A115178. Alternating sign version is A115179.
%F Number triangle T(n,k)=C(k)C(k,nk).
%e Triangle begins
%e .1,
%e .0, 1,
%e .0, 1, 2,
%e .0, 0, 4, 5,
%e .0, 0, 2, 15, 14,
%e .0, 0, 0, 15, 56, 42,
%e .0, 0, 0, 5, 84, 210, 132,
%e .0, 0, 0, 0, 56, 420, 792, 429
%K easy,nonn,tabl
%O 0,6
%A _Paul Barry_, Mar 14 2006
