A114117 - OEIS

%I #10 Sep 09 2024 09:36:28

%S 1,0,1,-2,1,1,-1,-1,1,1,0,-2,0,1,1,0,-1,-1,0,1,1,0,0,-2,0,0,1,1,0,0,

%T -1,-1,0,0,1,1,0,0,0,-2,0,0,0,1,1,0,0,0,-1,-1,0,0,0,1,1,0,0,0,0,-2,0,

%U 0,0,0,1,1,0,0,0,0,-1,-1,0,0,0,0,1,1,0,0,0,0,0,-2,0,0,0,0,0,1,1,0,0,0,0,0,-1,-1,0,0,0,0,0,1,1,0,0,0,0,0,0,-2,0,0,0,0,0,0,1,1

%N Inverse of 1's counting matrix A114116.

%C Row sums are (1,1,0,0,0,.....) with g.f. 1+x. Diagonal sums have g.f. (1-x^2-x^3)/(1-x^3). Product of A114115 and the first difference matrix (1-x,x).

%F T(n, k) = Sum_{j=0..n} Sum_{i=0..n} C(floor((n+i)/2), j)*C(j, floor((n+i)/2))*(2*C(0, j-k)-C(1, j-k)).

%e Triangle begins

%e   1;

%e   0, 1;

%e  -2, 1, 1;

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

%e   0,-2, 0, 1, 1;

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

%e   0, 0,-2, 0, 0, 1, 1;

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

%Y Cf. A114115, A114116.

%K easy,sign,tabl

%O 0,4

%A _Paul Barry_, Nov 13 2005