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

Author

N. J. A. Sloane, Jun 10 2013

Keywords

• nonn
• tabf

Examples

			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
...
		

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).

Crossrefs

Cf. A226505. Row sums = A000110.

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

Extensions

More terms from Alois P. Heinz, Mar 24 2016