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Matrix (1,x)-(x,x^2) in Riordan array notation.
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%I #8 Jul 30 2023 17:23:53

%S 1,-1,1,0,0,1,0,-1,0,1,0,0,0,0,1,0,0,-1,0,0,1,0,0,0,0,0,0,1,0,0,0,-1,

%T 0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,-1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,

%U 0,0,0,0,0,-1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1

%N Matrix (1,x)-(x,x^2) in Riordan array notation.

%C Row sums are 1,0,1,0,1,0... Diagonal sums are A115360. Inverse is A115361.

%F Number triangle T(n, k)=if(n=k, 1, 0) OR if(n=2k+1, -1, 0).

%e Triangle begins:

%e 1;

%e -1, 1;

%e 0, 0, 1;

%e 0, -1, 0, 1;

%e 0, 0, 0, 0, 1;

%e 0, 0, -1, 0, 0, 1;

%e 0, 0, 0, 0, 0, 0, 1;

%e 0, 0, 0, -1, 0, 0, 0, 1;

%e 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 0, 0, 0, 0, -1, 0, 0, 0, 0, 1;

%e ...

%o (PARI) tabl(nn) = {T = matrix(nn, nn, n, k, n--; k--; if ((n==k), 1, if (n==2*k+1, -1, 0))); for (n=1, nn, for (k=1, n, print1(T[n, k], ", ");); print(););} \\ _Michel Marcus_, Mar 28 2015

%K easy,sign,tabl

%O 0,1

%A _Paul Barry_, Jan 21 2006