A126258 Triangle generated by Pascal's rule with left diagonal = [1,0,2,0,3,0,4,...] (A000027 with interpolated zeros) and right diagonal = [1,1,1,1,1,...].

1, 0, 1, 2, 1, 1, 0, 3, 2, 1, 3, 3, 5, 3, 1, 0, 6, 8, 8, 4, 1, 4, 6, 14, 16, 12, 5, 1, 0, 10, 20, 30, 28, 17, 6, 1, 5, 10, 30, 50, 58, 45, 23, 7, 1, 0, 15, 40, 80, 108, 103, 68, 30, 8, 1, 6, 15, 55, 120, 188, 211, 171, 98, 38, 9, 1, 0, 21, 70, 175, 308, 399, 382, 269, 136, 47, 10, 1

Offset: 0

Author

Philippe Deléham, Mar 08 2007

Keywords

• nonn
• tabl
• easy

Examples

			Triangle begins:
  1;
  0, 1;
  2, 1, 1;
  0, 3, 2, 1;
  3, 3, 5, 3, 1;
  0, 6, 8, 8, 4, 1;
  4, 6, 14, 16, 12, 5, 1;
  0, 10, 20, 30, 28, 17, 6, 1;
		

Crossrefs

Cf. A034299, A116914.

Formula

T(2*n,n) = A116914(n).

Sum_{k=0..n} T(n,k) = A034299(n).

Extensions

More terms from Jason Yuen, Sep 19 2024