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
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).
Extensions
More terms from Alois P. Heinz, Mar 24 2016