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Triangle T(n,k), 0<=k<=n, read by rows, given by [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...] where DELTA is the operator defined in A084938.
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%I #8 Sep 08 2013 13:30:45

%S 1,0,1,0,1,2,0,1,5,5,0,1,8,20,14,0,1,11,44,75,42,0,1,14,77,208,275,

%T 132,0,1,17,119,440,910,1001,429,0,1,20,170,798,2244,3808,3640,1430,0,

%U 1,23,230,1309,4655,10659,15504,13260,4862,0,1,26,299,2000

%N Triangle T(n,k), 0<=k<=n, read by rows, given by [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...] where DELTA is the operator defined in A084938.

%C Row sums : 1, 1, 3, 11, 43, 173, .... (see A026671).

%C Transposed version in A107842.

%F T(0, 0) = 1, T(n, 0) = 0 if n>0, T(n, k) = 0 if k>n, T(n, k) = (3n-3k+2)*binomial(3n-k-1, k-1)/(3n-2k+1).

%F T(n, n) = A000108(n), Catalan numbers.

%e Triangle begins:

%e 1;

%e 0, 1;

%e 0, 1, 2;

%e 0, 1, 5, 5;

%e 0, 1, 8, 20, 14;

%e 0, 1, 11, 44, 75, 42;

%e 0, 1, 14, 77, 208, 275, 132

%Y Cf. A000108, A000344, A003518, A000589, A107842.

%K easy,nonn,tabl

%O 0,6

%A _Philippe Deléham_, Aug 26 2005