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%I #3 Mar 30 2012 18:59:12
%S 1,1,1,0,2,1,0,1,2,1,0,0,2,2,1,0,0,1,2,2,1,0,0,0,2,2,2,1,0,0,0,1,2,2,
%T 2,1,0,0,0,0,2,2,2,2,1,0,0,0,0,1,2,2,2,2,1,0,0,0,0,0,2,2,2,2,2,1,0,0,
%U 0,0,0,1,2,2,2,2,2,1,0,0,0,0,0,0,2,2,2,2,2,2,1
%N An invertible partition matrix.
%C Row sums are n+1, A000027. Diagonal sums are 1,1,1,2,2,2,3,3,3,.... or A008620. Inverse is A114115. Product with first difference matrix (1-x,x) is A114117.
%F Number triangle T(n, k)=sum{j=0..n, C(floor((n+j)/2), k)C(k, floor((n+j)/2))}.
%e Triangle begins
%e 1.................=1
%e 1,1...............=2
%e 0,2,1.............=3
%e 0,1,2,1...........=4
%e 0,0,2,2,1.........=5
%e 0,0,1,2,2,1.......=6
%e 0,0,0,2,2,2,1.....=7
%e 0,0,0,1,2,2,2,1...=8
%K easy,nonn,tabl
%O 0,5
%A _Paul Barry_, Nov 13 2005
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