A322058 Irregular triangle read by rows: T(n,k) = number of 1324-avoiding permutations of length n >= 0 having k >= 0 inversions.

1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 5, 6, 5, 3, 1, 1, 2, 5, 10, 16, 20, 20, 15, 9, 4, 1, 1, 2, 5, 10, 20, 32, 51, 67, 79, 80, 68, 49, 29, 14, 5, 1, 1, 2, 5, 10, 20, 36, 61, 96, 148, 208, 268, 321, 351, 347, 308, 241, 165, 98, 49, 20, 6, 1, 1, 2, 5, 10, 20, 36, 65, 106, 171, 262, 397, 568, 784, 1019, 1264, 1478, 1628, 1681, 1619, 1441, 1173, 866, 574, 338, 174, 76, 27, 7, 1

Offset: 0

Author

N. J. A. Sloane, Dec 25 2018

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  1;
  1;
  1, 1;
  1, 2, 2,  1;
  1, 2, 5,  6,  5,  3,  1;
  1, 2, 5, 10, 16, 20, 20, 15,  9,  4,  1;
  1, 2, 5, 10, 20, 32, 51, 67, 79, 80, 68, 49, 29, 14, 5, 1;
  ...
		

References

• Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 769, Fig. 12.13.

Crossrefs

The rows appear to be converging to A000712.

Row sums are A061552.

Cf. A188919.

Extensions

More terms from Alois P. Heinz, Dec 27 2018