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Triangle T read by rows derived from the signed Pascal triangle and satisfying T = T^(-1).
0

%I #12 Feb 20 2020 13:59:19

%S -1,1,1,1,0,1,1,-1,3,-1,1,-2,6,-4,1,1,-3,10,-10,5,-1,1,-4,15,-20,15,

%T -6,1,1,-5,21,-35,35,-21,7,-1,1,-6,28,-56,70,-56,28,-8,1,1,-7,36,-84,

%U 126,-126,84,-36,9,-1

%N Triangle T read by rows derived from the signed Pascal triangle and satisfying T = T^(-1).

%F In the signed version of Pascal's triangle, add 2 to each term in the next to left column. The first row in Pascal's triangle is replaced by -1.

%e (1, -3, 3, -1) becomes (1, -1, 3, -1) by adding 2 to -3.

%e First few rows of the triangle are:

%e -1;

%e 1, 1;

%e 1, 0, 1;

%e 1, -1, 3, -1;

%e 1, -2, 6, -4, 1;

%e 1, -3, 10, -10, 5, -1;

%e 1, -4, 15, -20, 15, -6, 1;

%e ...

%Y Cf. A007318.

%K sign,tabl

%O 0,9

%A _Gary W. Adamson_, Nov 13 2019