%I #7 May 24 2021 23:34:12
%S 1,0,1,0,-1,1,0,0,-2,1,0,1,1,-3,1,0,-1,2,3,-4,1,0,0,-4,2,6,-5,1,0,1,2,
%T -9,0,10,-6,1,0,-1,3,9,-15,-5,15,-7,1,0,0,-6,3,24,-20,-14,21,-8,1,0,1,
%U 3,-18,-6,49,-21,-28,28,-9,1
%N T(n, k) = (-1)^(n - k)*binomial(n - 1, k - 1)*hypergeom([-(n - k)/2, -(n - k - 1)/2], [1 - n], 4). Triangle read by rows, T(n, k) for 0 <= k <= n.
%C The inverse of the Riordan array for directed animals A122896. Without the first column (1, 0, 0, ...) the inverse of the Motzkin triangle A064189.
%F Riordan_array (1, x / (1 + x + x^2)).
%e Triangle starts:
%e [0] 1;
%e [1] 0, 1;
%e [2] 0, -1, 1;
%e [3] 0, 0, -2, 1;
%e [4] 0, 1, 1, -3, 1;
%e [5] 0, -1, 2, 3, -4, 1;
%e [6] 0, 0, -4, 2, 6, -5, 1;
%e [7] 0, 1, 2, -9, 0, 10, -6, 1;
%e [8] 0, -1, 3, 9, -15, -5, 15, -7, 1;
%e [9] 0, 0, -6, 3, 24, -20, -14, 21, -8, 1.
%p T := (n,k) -> (-1)^(n-k)*binomial(n-1,k-1)*hypergeom([-(n-k)/2, -(n-k-1)/2], [1-n], 4): seq(seq(simplify(T(n, k)), k=0..n), n = 0..10);
%o (SageMath) # uses[riordan_array from A256893]
%o riordan_array(1, x / (1 + x + x^2), 10)
%Y A117569 (row sums).
%Y Cf. A122896, A064189.
%K sign,tabl
%O 0,9
%A _Peter Luschny_, May 23 2021