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A central binomial scaling of the Riordan array (1+x,x) (A097806).
0

%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