A226504 Irregular triangle read by rows: T(n,k) = number of set partitions of [1..n] with dimension k.

1, 1, 2, 4, 1, 8, 4, 3, 16, 12, 13, 9, 2, 32, 32, 42, 42, 35, 12, 8, 64, 80, 120, 145, 159, 133, 86, 52, 32, 6, 128, 192, 320, 440, 559, 600, 591, 440, 380, 248, 164, 48, 30, 256, 448, 816, 1240, 1745, 2154, 2503, 2529, 2358, 2112, 1828, 1314, 944, 468, 258, 150, 24

Offset

0,3

Links

Alois P. Heinz, Rows n = 0..50, flattened

B. Chern, P. Diaconis, D. M. Kane, R. C. Rhoades, Closed expressions for averages of set partition statistics, [PDF], 2013. Also arXiv:1304.4309 (2013).

Example

Triangle begins:
1
1
2
4 1
8 4 3
16 12 13 9 2
32 32 42 42 35 12 8
64 80 120 145 159 133 86 52 32 6
128 192 320 440 559 600 591 440 380 248 164 48 30
...

Crossrefs

Cf. A226505. Row sums = A000110.

Columns k=0-1 give: A011782, A001787(n-2) (for n>1).

Sequence in context: A112931 A121685 A125810 * A152195 A133156 A207538

Adjacent sequences: A226501 A226502 A226503 * A226505 A226506 A226507

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jun 10 2013

Extensions

More terms from Alois P. Heinz, Mar 24 2016

Status

approved