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%I #18 Nov 18 2023 09:34:24
%S 1,14,805,208152,250409016,1423422089804,38533696399916432,
%T 4988815527667401921920,3096067500138473517778378240,
%U 9222307552079662925642825622240000,131945758198070262889738914466064452265625,9070830675953705403006049148134626173379375000000
%N Number of binary operators defined on the finite chain L_n={0,1,...n}, C:L_n^2-> L_n, which are increasing in each argument, and satisfy the boundary conditions C(0,n)=C(n,0)=0 and C(n,n)=n.
%H M. Munar, S. Massanet and D. Ruiz-Aguilera, <a href="https://doi.org/10.1016/j.ins.2022.10.121">On the cardinality of some families of discrete connectives</a>, Information Sciences, Volume 621, 2023, 708-728.
%F a(n) = Product_{i=1..n} Product_{j=1..n} Product_{k=1..n} (i+j+k-1)/(i+j+k-2) - Product_{i=1..n} Product_{j=1..n} Product_{k=1..n-1} (i+j+k-1)/(i+j+k-2).
%F a(n) = A008793(n+1) - A071095(n). - _Vaclav Kotesovec_, Nov 18 2023
%t Table[Product[Product[Product[(i + j + k - 1)/(i + j + k - 2), {k, 1, n}], {j, 1, n}], {i, 1, n}] - Product[Product[Product[(i + j + k - 1)/(i + j + k - 2), {k, 1, n - 1}], {j, 1, n}], {i, 1, n}], {n, 1, 15}]
%Y Cf. A008793, A071095.
%K nonn
%O 1,2
%A _Marc Munar_, Feb 14 2023