A096921 Triangle array of binomial coefficients.

1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 3, 3, 6, 1, 1, 3, 4, 6, 10, 1, 1, 4, 4, 10, 10, 20, 1, 1, 4, 5, 10, 15, 20, 35, 1, 1, 5, 5, 15, 15, 35, 35, 70, 1, 1, 5, 6, 15, 21, 35, 56, 70, 126, 1, 1, 6, 6, 21, 21, 56, 56, 126, 126, 252, 1, 1, 6, 7, 21, 28, 56, 84, 126, 210, 252, 462

Offset: 0

Author

Paul Barry, Jul 15 2004

Keywords

• easy
• nonn
• tabl

Examples

			Triangle begins:
      k=0  1  2  3  4  5
  n=0:  1;
  n=1:  1, 1;
  n=2:  1, 1, 2;
  n=3:  1, 1, 2, 3;
  n=4:  1, 1, 3, 3, 6;
  n=5:  1, 1, 3, 4, 6, 10;
  ...
		

Crossrefs

Cf. A026010 (row sums), A016116 (diagonal sums), A001405 (main diagonal).

Programs

Mathematica

T[n_, k_]=Binomial[Floor[(n+k)/2], Floor[k/2]]; Table[T[n,k],{n,0,11},{k,0,n}] (* Stefano Spezia, Aug 23 2022 *)

PARI

T(n, k) = binomial((n+k)\2, k\2); \\ Michel Marcus, Oct 29 2022

Formula

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