%I #14 Jul 29 2023 03:28:38
%S 1,-1,1,1,-1,1,0,1,-1,1,1,0,1,-1,1,0,1,0,1,-1,1,2,0,1,0,1,-1,1,0,2,0,
%T 1,0,1,-1,1,3,0,2,0,1,0,1,-1,1,1,3,0,2,0,1,0,1,-1,1,4,1,3,0,2,0,1,0,1,
%U -1,1,2,4,1,3,0,2,0,1,0,1,-1,1
%N Triangle read by rows: A000012^(-2) * A027293 as infinite lower triangular matrices.
%C Row sums = A002865, (1, 0, 1, 1, 2, 2, 4, 4, 7, 8,...).
%C This triangle is the lower right half of a Toeplitz matrix. Each column of this triangle has the form [1, -1] U A053445. - _Georg Fischer_, Jul 28 2023
%F A000012^(-1) is the pairwise difference operator, and A027293 = a triangle with A000041 in every column.
%F Equals A185018 * A027293 since A000012^2 = A004736 and A004736^(-1) = A185018. - _Georg Fischer_, Jul 28 2023
%e First few rows of the triangle =
%e 1;
%e -1, 1;
%e 1, -1, 1;
%e 0, 1, -1, 1;
%e 1, 0, 1, -1, 1;
%e 0, 1, 0, 1, -1, 1;
%e 2, 0, 1, 0, 1, -1, 1;
%e 0, 2, 0, 1, 0, 1, -1, 1;
%e 3, 0, 2, 0, 1, 0, 1, -1, 1;
%e 1, 3, 0, 2, 0, 1, 0, 1, -1, 1;
%e 4, 1, 3, 0, 2, 0, 1, 0, 1, -1, 1;
%e 2, 4, 1, 3, 0, 2, 0, 1, 0, 1, -1, 1;
%e ...
%Y Cf. A000012, A000041, A002865, A004736, A027293, A053445, A185018.
%K tabl,sign
%O 0,22
%A _Gary W. Adamson_, Nov 11 2008