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A226505
Irregular triangle read by rows: T(n,k) = number of set partitions of [1..n] with intertwining weight k.
1
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
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
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Jun 10 2013
STATUS
approved