A226505 Irregular triangle read by rows: T(n,k) = number of set partitions of [1..n] with intertwining weight k.

1, 1, 2, 5, 14, 1, 42, 9, 1, 132, 55, 14, 2, 429, 286, 120, 35, 6, 1, 1430, 1365, 819, 364, 119, 35, 7, 1, 4862, 6188, 4900, 2940, 1394, 586, 203, 59, 13, 2, 16796, 27132, 26928, 20400, 12576, 6846, 3246, 1358, 493, 153, 38, 8, 1

Offset

0,3

Links

Table of n, a(n) for n=0..49.

B. Chern, P. Diaconis, D. M. Kane, and R. C. Rhoades, Closed expressions for averages of set partition statistics, arXiv:1304.4309 [math.CO], 2013.

Example

Triangle begins:
1
1
2
5
14 1
42 9 1
132 55 14 2
429 286 120 35 6 1
1430 1365 819 364 119 35 7 1
4862 6188 4900 2940 1394 586 203 59 13 2
16796 27132 26928 20400 12576 6846 3246 1358 493 153 38 8 1
...

Crossrefs

Cf. A226504. First two columns are A000108, A030053.

Row sums give A000110.

Sequence in context: A190478 A155838 A166405 * A370235 A279176 A279876

Adjacent sequences: A226502 A226503 A226504 * A226506 A226507 A226508

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jun 10 2013

Status

approved