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%I #17 Mar 24 2016 16:26:58
%S 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,
%T 133,86,52,32,6,128,192,320,440,559,600,591,440,380,248,164,48,30,256,
%U 448,816,1240,1745,2154,2503,2529,2358,2112,1828,1314,944,468,258,150,24
%N Irregular triangle read by rows: T(n,k) = number of set partitions of [1..n] with dimension k.
%H Alois P. Heinz, <a href="/A226504/b226504.txt">Rows n = 0..50, flattened</a>
%H B. Chern, P. Diaconis, D. M. Kane, R. C. Rhoades, <a href="http://arxiv.org/abs/1304.4309">Closed expressions for averages of set partition statistics</a>, <a href="http://math.stanford.edu/~rhoades/FILES/setpartitions.pdf">[PDF]</a>, 2013. Also arXiv:1304.4309 (2013).
%e Triangle begins:
%e 1
%e 1
%e 2
%e 4 1
%e 8 4 3
%e 16 12 13 9 2
%e 32 32 42 42 35 12 8
%e 64 80 120 145 159 133 86 52 32 6
%e 128 192 320 440 559 600 591 440 380 248 164 48 30
%e ...
%Y Cf. A226505. Row sums = A000110.
%Y Columns k=0-1 give: A011782, A001787(n-2) (for n>1).
%K nonn,tabf
%O 0,3
%A _N. J. A. Sloane_, Jun 10 2013
%E More terms from _Alois P. Heinz_, Mar 24 2016
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