%I #6 Apr 11 2013 09:38:18
%S 1,1,1,0,1,2,0,0,2,3,0,0,0,3,6,0,0,0,0,6,10,0,0,0,0,0,10,20,0,0,0,0,0,
%T 0,20,35,0,0,0,0,0,0,0,35,70,0,0,0,0,0,0,0,0,70,126,0,0,0,0,0,0,0,0,0,
%U 126,252
%N A central binomial scaling of the Riordan array (1+x,x) (A097806).
%C Row sums are A050168. Diagonal sums are A001045 doubled. Row sums of inverse are 1/C(2n,n) aerated. Applications to other sequences are obvious.
%F Number triangle T(n,k)=C(k,floor(k/2))*sum{j=0..n, (-1)^(n-j)C(n,j)C(j+1,k+1)}
%e Triangle begins
%e .1,
%e .1, 1,
%e .0, 1, 2,
%e .0, 0, 2, 3,
%e .0, 0, 0, 3, 6,
%e .0, 0, 0, 0, 6, 10,
%e .0, 0, 0, 0, 0, 10, 20,
%e .0, 0, 0, 0, 0, 0, 20, 35,
%e .0, 0, 0, 0, 0, 0, 0, 35, 70,
%e .0, 0, 0, 0, 0, 0, 0, 0, 70, 126,
%e .0, 0, 0, 0, 0, 0, 0, 0, 0, 126, 252
%K easy,nonn,tabl
%O 0,6
%A _Paul Barry_, Sep 18 2006