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A symmetric Catalan based triangle.
2

%I #5 Feb 26 2014 09:54:35

%S 1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,2,1,1,1,1,2,5,2,1,1,1,1,2,5,5,2,

%T 1,1,1,1,2,5,14,5,2,1,1,1,1,2,5,14,14,5,2,1,1,1,1,2,5,14,42,14,5,2,1,

%U 1,1,1,2,5,14,42,42,14,5,2,1,1,1,1,2,5,14,42,132,42,14,5,2,1,1

%N A symmetric Catalan based triangle.

%C Central coefficients are A000108. Row sums are A155051.

%C Image under Riordan array ((1+x)/(1-x),x)^{-1} is A155052.

%F Number triangle T(n,k)=sum{j=0..n, [j<=k]*[j<=n-k]*(ct(j+1)-ct(j))} where ct(n):=if(n=0,0,A000108(n-1)).

%F T(n,k) = A000108(min(k, n-k)). - _Philippe Deléham_, Feb 26 2014

%e Triangle begins

%e 1,

%e 1, 1,

%e 1, 1, 1,

%e 1, 1, 1, 1,

%e 1, 1, 2, 1, 1,

%e 1, 1, 2, 2, 1, 1,

%e 1, 1, 2, 5, 2, 1, 1,

%e 1, 1, 2, 5, 5, 2, 1, 1,

%e 1, 1, 2, 5, 14, 5, 2, 1, 1,

%e 1, 1, 2, 5, 14, 14, 5, 2, 1, 1,

%e 1, 1, 2, 5, 14, 42, 14, 5, 2, 1, 1

%Y Cf. A000108, A155051

%K easy,nonn,tabl

%O 0,13

%A _Paul Barry_, Jan 19 2009