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%I #27 Nov 18 2021 11:27:07
%S 1,1,1,1,3,1,1,7,6,1,1,15,26,10,1,1,31,100,69,15,1,1,63,366,412,150,
%T 21,1,1,127,1317,2305,1270,286,28,1,1,255,4743,12551,9920,3236,497,36,
%U 1,1,511,17275,67933,74525,33301,7210,806,45,1,1,1023,64029,370168,551232,325860,93926,14540,1239,55,1,1,2047,242371,2046980,4072130,3109628,1151416,232891,27147,1825,66,1
%N Triangle read by rows: T(n,k) (n>=1, 1 <= k <= n) = number of n-element unlabeled interval posets of height k.
%H Soheir M. Khamis, <a href="https://doi.org/10.1016/S0012-365X(03)00106-7">Height counting of unlabeled interval and N-free posets</a>, Discrete Math. 275 (2004), no. 1-3, 165-175.
%H Soheir Mohamed Khamis, <a href="https://doi.org/10.1007/s11083-011-9213-5">Exact Counting of Unlabeled Rigid Interval Posets Regarding or Disregarding Height</a>, Order 29, pp. 443-461 (2012).
%e Triangle begins
%e 1
%e 1 1
%e 1 3 1
%e 1 7 6 1
%e 1 15 26 10 1
%e 1 31 100 69 15 1
%e 1 63 366 412 150 21 1
%e 1 127 1317 2305 1270 286 28 1
%e 1 255 4743 12551 9920 3236 497 36 1
%e 1 511 17275 67933 74525 33301 7210 806 45 1
%e ...
%Y Row sums give A022493. Cf. A193357.
%K nonn,tabl
%O 1,5
%A _N. J. A. Sloane_, Aug 26 2011
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