%I #13 Jan 25 2020 18:12:15

%S 1,0,1,0,1,1,0,1,3,1,0,1,6,6,1,0,1,10,19,10,1,0,1,15,45,45,15,1,0,1,

%T 21,90,141,90,21,1,0,1,28,161,357,357,161,28,1,0,1,36,266,784,1107,

%U 784,266,36,1,0,1,45,414,1554,2907,2907,1554,414,45,1,0,1,55,615,2850,6765,8953

%N Triangle T(n,k), 0 <= k <= n, read by rows given by [0, 1, 0, 1, 0, 0, 0, 0, 0, ...] DELTA [1, 0, 1, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938.

%C Subtriangle (1 <= k <= n) is in A056241.

%F T(2*k-1,k) = A082758(k-1)for k >= 1.

%F Sum_{k=0..n} T(n,k) = A124302(n); see also A007051.

%F Sum_{k=0..n} (-1)^(n-k)*T(n,k) = A117569(n).

%F G.f.: (1-x*(y+2)+x^2)/(1-2x*(1+y)+(1+y+y^2)*x^2). - _Philippe Deléham_, Oct 30 2011

%e Triangle begins:

%e 1;

%e 0, 1;

%e 0, 1, 1;

%e 0, 1, 3, 1;

%e 0, 1, 6, 6, 1;

%e 0, 1, 10, 19, 10, 1;

%e 0, 1, 15, 45, 45, 15, 1;

%e 0, 1, 21, 90, 141, 90, 21, 1;

%e 0, 1, 28, 161, 357, 357, 161, 28, 1;

%e 0, 1, 36, 266, 784, 1107, 784, 255, 36, 1;

%e 0, 1, 45, 414, 1554, 2907, 2907, 1554, 414, 45, 1;

%e 0, 1, 55, 615, 2850, 6765, 8953, 6765, 2850, 615, 55, 1;

%Y Columns: A000007, A000012, A000217, A005712, A005714, A005716.

%Y Cf. A027907, A056241.

%K nonn,tabl

%O 0,9

%A _Philippe Deléham_, Oct 30 2006