A127967 A right-skewed Pascal triangle, with interspersed 1's on main diagonal.

1, 1, 1, 1, 0, 1, 1, 0, 2, 1, 1, 0, 3, 0, 1, 1, 0, 4, 0, 3, 1, 1, 0, 5, 0, 6, 0, 1, 1, 0, 6, 0, 10, 0, 4, 1, 1, 0, 7, 0, 15, 0, 10, 0, 1, 1, 0, 8, 0, 21, 0, 20, 0, 5, 1, 1, 0, 9, 0, 28, 0, 35, 0, 15, 0, 1, 1, 0, 10, 0, 36, 0, 56, 0, 35, 0, 6, 1

Offset: 0

Author

Paul Barry, Feb 09 2007

Keywords

• easy
• nonn
• tabl

Comments

Linked to Fibonacci numbers by row sums A127968. Inverse A127969 is linked to Genocchi numbers by its first column.

Examples

			Triangle begins
  1;
  1, 1;
  1, 0,  1;
  1, 0,  2, 1;
  1, 0,  3, 0,  1;
  1, 0,  4, 0,  3, 1;
  1, 0,  5, 0,  6, 0,  1;
  1, 0,  6, 0, 10, 0,  4, 1;
  1, 0,  7, 0, 15, 0, 10, 0,  1;
  1, 0,  8, 0, 21, 0, 20, 0,  5, 1;
  1, 0,  9, 0, 28, 0, 35, 0, 15, 0,  1;
  1, 0, 10, 0, 36, 0, 56, 0, 35, 0,  6, 1;
  1, 0, 11, 0, 45, 0, 84, 0, 70, 0, 21, 0, 1;
		

Crossrefs

Cf. A127968, A127969.

Formula

Column k is generated by x^(-2)*(x*(1-x)^(-1/2))^(k+2), where non-integer values are set to 0; or, column k has g.f. x^k/(1-x)^(1+k/2) if k is even, x^k if k is odd.