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Triangle read by rows: T(n,k) (1 <= k <= n) = number of ascendingly generated semigroups of order n with k generators.
1

%I #17 Mar 02 2020 08:53:45

%S 1,2,8,3,37,113,4,145,1257,3492,5,452,9020,67394,183732,6,1374,60826,

%T 938194,6398792,17061118,7,3933,356023,30492722,466578957,3032145644,

%U 7743056064

%N Triangle read by rows: T(n,k) (1 <= k <= n) = number of ascendingly generated semigroups of order n with k generators.

%H Alex Bailey, Martin Finn-Sell, Robert Snocken, <a href="http://arxiv.org/abs/1409.2444">Subsemigroup, ideal and congruence growth of free semigroups</a>, arXiv preprint arXiv:1409.2444 [math.GR], 2014.

%e Triangle begins:

%e 1;

%e 2, 8;

%e 3, 37, 113;

%e 4, 145, 1257, 3492;

%e 5, 452, 9020, 67394, 183732;

%e 6, 1374, 60826, 938194, 6398792, 17061118;

%e 7, 3933, 356023, 30492722, 466578957, 3032145644, 7743056064;

%e ...

%Y Main diagonal is A023814. Column 2 is A256412.

%K nonn,tabl,more

%O 1,2

%A _N. J. A. Sloane_, Apr 03 2015