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

2,2

Links

Table of n, a(n) for n=2..83.

Example

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;

Mathematica

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

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.

Sequence in context: A008734 A226649 A053445 * A290982 A346034 A353949

Adjacent sequences: A175987 A175988 A175989 * A175991 A175992 A175993

Keyword

nonn,tabf,easy,less

Author

Roger L. Bagula, Dec 06 2010

Extensions

Definition clarified by Harvey P. Dale, May 08 2023

Status

approved