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%I #3 Mar 30 2012 17:25:33
%S 1,0,1,1,0,2,0,2,0,3,2,0,6,0,6,0,5,0,12,0,10,5,0,18,0,30,0,20,0,14,0,
%T 42,0,60,0,35,14,0,56,0,120,0,140,0,70,0,42,0,144,0,270,0,280,0,126
%N Convolution triangle, A053121 * (A001405 * 0^(n-k))
%C Row sums = A145974: (1, 1, 3, 5, 14, 27, 73,...).
%F Convolution triangle, A053121 * (A001405 * 0^(n-k)).
%F A053121 = the aerated Catalan triangle and (A001405 * 0^(n-k) = an
%F infinite lower triangular matrix with A001405 as the main diagonal and
%F the rest zeros.
%e First few rows of the triangle =
%e 1;
%e 0, 1;
%e 1, 0, 2;
%e 0, 2, 0, 3;
%e 2, 0, 6, 0, 6;
%e 0, 5, 0, 12, 0, 10;
%e 5, 0, 18, 0, 30, 0, 20;
%e 0, 14, 0, 42, 0, 60, 0, 35;
%e 14, 0, 56, 0, 120, 0, 140, 0, 70;
%e 0, 42, 0, 144, 0, 270, 0, 280, 0, 126;
%e 42, 0, 180, 0, 450, 0, 700, 0, 630, 0, 252;
%e ...
%e Example: Row 4 = (2, 0, 6, 0, 6) = termwise products of (2, 0, 3, 0, 1) and (1, 1, 2, 3, 6).
%K nonn,tabl
%O 0,6
%A _Gary W. Adamson_, Dec 28 2008
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