A171698 Square 'central binomial coefficients'-array read by antidiagonals.

1, 1, 1, 2, 2, 2, 6, 6, 4, 4, 20, 20, 14, 8, 8, 70, 70, 50, 30, 16, 16, 252, 252, 182, 112, 62, 32, 32, 924, 924, 672, 420, 238, 126, 64, 64, 3432, 3432, 2508, 1584, 912, 492, 254, 128, 128, 12870, 12870, 9438, 6006, 3498, 1914, 1002, 510, 256, 256

Offset

0,4

Comments

Antidiagonals sum up to A000984.

Links

Table of n, a(n) for n=0..54.

Juan B. Gil, Oscar A. Lopez, and Michael D. Weiner, On separable permutations and three other pairs in the Schröder class, arXiv:2603.25528 [math.CO], 2026. See p. 13.

Example

Example with 0's added:
  0,1,1,2,4,8,..
  0,1,2,4,8,16,..
  0,2,6,14,30,..
Row 2 (binomial): 0+1=1,1+1=2,...
Row 3 (trinomial): 0+1+1=2,2+2+2=6,6+4+4=14...

Crossrefs

Cf. A000984, A011782, A009766, A007318.

Main diaginal gives A393178.

Sequence in context: A242010 A283673 A198472 * A339385 A395725 A080969

Adjacent sequences: A171695 A171696 A171697 * A171699 A171700 A171701

Keyword

nonn,tabl

Author

Mark Dols, Dec 15 2009

Extensions

Offset set to 0 by Alois P. Heinz, Apr 01 2026

Status

approved