%I #8 Apr 25 2016 13:18:26
%S 1,1,1,1,2,2,1,3,6,3,1,4,12,12,3,1,5,20,30,15,0,1,6,30,60,
%T 45,0,10,1,7,42,105,105,0,70,35,1,8,56,168,210,0,280,280,90
%N Triangle, row sums = A005614, the rabbit sequence.
%F Binomial transform of the infinite matrix with the diagonalized sequence A124841.
%e First few rows of the triangle are:
%e 1;
%e 1, 1;
%e 1, 2, 2;
%e 1, 3, 6, 3;
%e 1, 4, 12, 12, 3;
%e 1, 5, 20, 30, 15, 0;
%e 1, 6, 30, 60, 45, 0, 10;
%e ...
%e 4th term of the rabbit sequence (1, 0, 1, 1, 0...) = 1 = sum of row 4 terms: (1,  3 + 6  3).
%Y Cf. A124841.
%K sign,tabl
%O 1,5
%A _Gary W. Adamson_, Nov 10 2006
