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A226504 Irregular triangle read by rows: T(n,k) = number of set partitions of [1..n] with dimension k. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 27 16:20 EDT 2020. Contains 337383 sequences. (Running on oeis4.)