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%I #19 Jan 25 2020 18:12:41
%S 1,1,1,2,3,1,1,3,3,1,2,7,9,5,1,1,5,10,10,5,1,2,11,25,30,20,7,1,1,7,21,
%T 35,35,21,7,1,2,15,49,91,105,77,35,9,1,1,9,36,84,126,126,84,36,9,1
%N A133566 * A007318 as infinite lower triangular matrices.
%C Row sums = A122756: (1, 2, 6, 8, 24, 32, 96, ...).
%C With offset (0,4); triangle T(n,k), 0 <= k <= n, given by [1,1,-3,1,0,0,0,0,0,0,0,...] DELTA [1,0,-2,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Dec 15 2007
%F T(n,k) = T(n-2,k) + 2*T(n-2,k-1) + T(n-2,k-2), T(0,0) = 1, T(1,0) = T(1,1) = 1, T(2,0) = 2, T(2,1) = 3, T(2,2) = 1, T(n,k) = 0 if k < 0 or if k > n. - _Philippe Deléham_, Sep 17 2014
%F G.f.: (-1-x-x*y-x^2-x^2*y)/((x*y+1+x)*(-1+x+x*y)). - _R. J. Mathar_, Aug 12 2015
%e First few rows of the triangle:
%e 1;
%e 1, 1;
%e 2, 3, 1;
%e 1, 3, 3, 1;
%e 2, 7, 9, 5, 1;
%e 1, 5, 10, 10, 5, 1;
%e 2, 11, 25, 30, 20, 7, 1;
%e 1, 7, 21, 35, 35, 21, 7, 1;
%e ...
%Y Cf. A133566, A122756.
%K nonn,tabl
%O 1,4
%A _Gary W. Adamson_, Sep 16 2007
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