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%I #16 Dec 12 2024 15:30:49
%S 1,1,1,1,4,1,1,18,18,1,1,166,656,166,1,1,7579,189967,189967,7579,1,1,
%T 7828352
%N Triangle read by rows: T(n,k) is the number of functions on the Boolean lattice B_n satisfying f({}) =0, f([n])=k, and the Boolean growth rule: f(J union {i})-f(J) in {0,1} for all subsets J of [n]={1, ..., n} and all i in [n]\J, 0 <= k <= n.
%C For k=1, these numbers are the Dedekind numbers A007153 counting the number of monotone Boolean functions or equivalently antichains of subsets of an n-set containing at least one nonempty set.
%H Sara Billey and Matjaž Konvalinka, <a href="https://arxiv.org/abs/2412.03236">Generalized rank functions and quilts of alternating sign matrices</a>, arXiv:2412.03236 [math.CO], 2024. See p. 32.
%e Triangle begins:
%e 1;
%e 1, 1;
%e 1, 4, 1;
%e 1, 18, 18, 1;
%e 1, 166, 656, 166, 1;
%e 1, 7579, 189967, 189967, 7579, 1;
%e ...
%Y Cf. A000372, A007153, A374820, A374821, A374822, A297622, A374824.
%K nonn,tabl,more
%O 0,5
%A _Sara Billey_ and _Matjaz Konvalinka_, Jul 25 2024