A227159 Triangle read by rows: number of 321-avoiding ordered set partitions of [n] into k blocks, n>=1, 1<=k<=n.

1, 1, 2, 1, 6, 5, 1, 14, 27, 14, 1, 30, 99, 112, 42, 1, 62, 307, 564, 450, 132, 1, 126, 867, 2284, 2895, 1782, 429, 1, 254, 2307, 8124, 14485, 13992, 7007, 1430, 1, 510, 5891, 26492, 62085, 83446, 65065, 27456, 4862, 1, 1022, 14595, 81148, 239269, 418578, 450905, 294632, 107406, 16796

Offset

1,3

Links

Table of n, a(n) for n=1..55.

Anisse Kasraoui, Pattern avoidance in ordered set partitions and words, arXiv:1307.0495 [math.CO], 2013.

Example

Triangle starts
1
1 2
1 6 5
1 14 27 14
1 30 99 112 42
1 62 307 564 450 132
1 126 867 2284 2895 1782 429
1 254 2307 8124 14485 13992 7007 1430
1 510 5891 26492 62085 83446 65065 27456 4862
1 1022 14595 81148 239269 418578 450905 294632 107406 16796

Mathematica

T[n_, k_] := (-1)^(k-1) k + Sum[(-1)^(k-j) Binomial[k, j+2] 2^(n-2j) Sum[(2 j-2i+1)/(j+1) Binomial[2i, i] Binomial[2(j-i), j-i] Binomial[n+2i, 2i], {i, 0, j}], {j, 0, k-2}];
Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jul 23 2018, from Kasraoui theorem 3.5 *)

Crossrefs

Sequence in context: A108767 A046817 A193817 * A294439 A008970 A055896

Adjacent sequences: A227156 A227157 A227158 * A227160 A227161 A227162

Keyword

nonn,tabl

Author

Joerg Arndt, Jul 03 2013

Status

approved