A175990 Irregular triangle read by rows: t(n,m) = binomial(n-m-1,m+1) for 0 <= m <= floor((n-1)/2).

1, 2, 0, 3, 1, 4, 3, 0, 5, 6, 1, 6, 10, 4, 0, 7, 15, 10, 1, 8, 21, 20, 5, 0, 9, 28, 35, 15, 1, 10, 36, 56, 35, 6, 0, 11, 45, 84, 70, 21, 1, 12, 55, 120, 126, 56, 7, 0, 13, 66, 165, 210, 126, 28, 1, 14, 78, 220, 330, 252, 84, 8, 0, 15, 91, 286, 495, 462, 210, 36, 1, 16, 105, 364, 715, 792, 462, 120, 9, 0, 17, 120

Offset: 2

Author

Roger L. Bagula, Dec 06 2010

Keywords

• nonn
• tabf
• easy
• less

Examples

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

Crossrefs

Row sums are A000071.

Essentially the same as A011973 (removing first column). Elimination of each 2nd row yields essentially A054142 or A121314. Interleaving with zeros gives A052553.

Padding with an initial column of 1's and more zeros yields A169803. Signed variants are A115139 and A124033.

Programs

Mathematica

Table[Binomial[n-m-1,m+1],{n,2,15},{m,0,Floor[(n-1)/2]}]//Flatten (* Harvey P. Dale, May 08 2023 *)

Extensions

Definition clarified by Harvey P. Dale, May 08 2023