A122935 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.

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, 21, 90, 141, 90, 21, 1, 0, 1, 28, 161, 357, 357, 161, 28, 1, 0, 1, 36, 266, 784, 1107, 784, 266, 36, 1, 0, 1, 45, 414, 1554, 2907, 2907, 1554, 414, 45, 1, 0, 1, 55, 615, 2850, 6765, 8953

Offset: 0

Author

Philippe Deléham, Oct 30 2006

Keywords

• nonn
• tabl

Comments

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

Examples

			Triangle begins:
  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, 21,  90,  141,   90,   21,    1;
  0, 1, 28, 161,  357,  357,  161,   28,    1;
  0, 1, 36, 266,  784, 1107,  784,  255,   36,   1;
  0, 1, 45, 414, 1554, 2907, 2907, 1554,  414,  45,  1;
  0, 1, 55, 615, 2850, 6765, 8953, 6765, 2850, 615, 55, 1;
		

Crossrefs

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

Cf. A027907, A056241.

Formula

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

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

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

G.f.: (1-x*(y+2)+x^2)/(1-2x*(1+y)+(1+y+y^2)*x^2). - Philippe Deléham, Oct 30 2011