%I #11 Apr 15 2016 13:44:27

%S 1,1,1,4,2,1,16,11,3,1,81,48,19,4,1,441,266,93,28,5,1,2601,1492,549,

%T 152,38,6,1,16129,9042,3211,947,226,49,7,1

%N Triangle read by rows: T(n,r) (0 <= r <= n) = number of idempotents of rank r in the Motzkin monoid M_n.

%H I. Dolinka, J. East et al, <a href="http://arxiv.org/abs/1507.04838">Idempotent Statistics of the Motzkin and Jones Monoids</a>, arXiv: 1507.04838 (2015), Table 2.

%e Triangle begins:

%e 1,

%e 1,1,

%e 4,2,1,

%e 16,11,3,1,

%e 81,48,19,4,1,

%e 441,266,93,28,5,1,

%e 2601,1492,549,152,38,6,1,

%e 16129,9042,3211,947,226,49,7,1,

%e ...

%Y First column is A001006(n)^2.

%Y Row sums are A256672.

%K nonn,tabl,more

%O 0,4

%A _N. J. A. Sloane_, Mar 13 2016