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%I #12 Oct 25 2021 11:10:32
%S 1,1,0,1,1,0,1,2,0,0,1,3,1,0,0,1,4,3,0,0,0,1,5,5,1,0,0,0,1,6,7,4,0,0,
%T 0,0,1,7,9,7,1,0,0,0,0,1,8,11,10,5,0,0,0,0,0,1,9,13,13,9,1,0,0,0,0,0,
%U 1,10,15,16,13,6,0,0,0,0,0,0,1,11,17,19,17,11,1,0,0,0,0,0,0,1,12,19,22,21,16,7,0,0,0,0,0,0,0
%N Rectangle R(i,j) read by ascending antidiagonals: column j has j-1 zeros followed by numbers congruent to 1 mod j-1.
%C The number of occurrences of k is the number of divisors of k-1, for k>=2. Column 1 of the inverse of this infinite matrix begins with (1,-1,1,-1,2,-6,24,-120,6!,-7!,8!,-9!,...). The remaining columns are likewise expressible in terms of factorials.
%F R(i, j) = (i-j)*(j-1)+1 if 1<=j<=i; R(i, j)=0 if j>=i+1.
%e Northwest corner:
%e 1 0 0 0 0 0
%e 1 1 0 0 0 0
%e 1 2 1 0 0 0
%e 1 3 3 1 0 0
%e 1 4 5 4 1 0
%e 1 5 7 7 5 1
%Y Cf. A077028.
%K nonn,tabl
%O 1,8
%A _Clark Kimberling_, Oct 19 2002
%E Definition amended by _Georg Fischer_, Oct 25 2021
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