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%I #4 Mar 03 2013 14:17:30
%S 1,1,1,1,0,1,1,2,0,1,1,0,0,0,1,1,3,1,0,0,1,1,0,0,0,0,0,1,1,4,0,3,0,0,
%T 0,1,1,0,1,0,0,0,0,0,1,1,5,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,1,6,
%U 1,6,0,4,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1
%N Triangle read by rows, A167269 columns aerated with k zeros
%C Row sums = A167272: (1, 2, 2, 4, 2, 6, 2, 9,k 3, 8, 2, 19,...).
%C Product of columns = A167273: (1, 1, 3, 4, 10, 13, 28, 37, 73,...).
%F Given triangle A167269, T(n,k), aerate column terms with k zeros.
%e First few rows of the triangle =
%e 1,
%e 1, 1;
%e 1, 0, 1;
%e 1, 2, 0, 1;
%e 1, 0, 0, 0, 1;
%e 1, 3, 1, 0, 0, 1;
%e 1, 0, 0, 0, 0, 0, 1;
%e 1, 4, 0, 3, 0, 0, 0, 1;
%e 1, 0, 1, 0, 0, 0, 0, 0, 1;
%e 1, 5, 0, 0, 1, 0, 0, 0, 0, 1;
%e 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e 1, 6, 1, 6, 0, 4, 0, 0, 0, 0, 0, 1;
%e 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e 1, 7, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1;
%e 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e 1, 8, 0, 10, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 1;
%e ...
%Y Cf. A167269, A167272, A167273
%K nonn,tabl
%O 0,8
%A _Gary W. Adamson_ & _Mats Granvik_, Oct 31 2009