A109223 Number triangle related to the Fibonacci polynomials.

1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 5, 1, 1, 1, 6, 5, 7, 1, 1, 1, 6, 15, 7, 9, 1, 1, 1, 10, 15, 28, 9, 11, 1, 1, 1, 10, 35, 28, 45, 11, 13, 1, 1, 1, 15, 35, 84, 45, 66, 13, 15, 1, 1, 1, 15, 70, 84, 165, 66, 91, 15, 17, 1, 1, 1, 21, 70, 210, 165, 286, 91, 120, 17, 19, 1, 1, 1, 21, 126, 210

Offset: 0

Author

Paul Barry, Jun 22 2005

Keywords

• easy
• nonn
• tabl

Comments

Riordan array (1/(1-x), x/(1-x^2)^2). Row-reversal of number triangle A109221. Diagonals form a repeated version of A054142. Row sums are A109222. Diagonal sums are A094967.

Examples

			Rows begin
  1;
  1,  1;
  1,  1,  1;
  1,  3,  1,  1;
  1,  3,  5,  1,  1;
  1,  6,  5,  7,  1,  1;
  1,  6, 15,  7,  9,  1,  1;
		

Programs

Maple

A109223 := proc(n,k): binomial(floor((n+k)/2)+k, 2*k) end: seq(seq(A109223(n,k), k=0..n), n=0..11); # Johannes W. Meijer, Aug 14 2011

Formula

T(n,k) = binomial(floor((n+k)/2)+k, 2*k)

T(n,k) = A065941(n+k,n-k). - Johannes W. Meijer, Aug 14 2011