A360612 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.

1, 14, 805, 208152, 250409016, 1423422089804, 38533696399916432, 4988815527667401921920, 3096067500138473517778378240, 9222307552079662925642825622240000, 131945758198070262889738914466064452265625, 9070830675953705403006049148134626173379375000000

Offset: 1

Author

Marc Munar, Feb 14 2023

Keywords

• nonn

Links

• M. Munar, S. Massanet and D. Ruiz-Aguilera, On the cardinality of some families of discrete connectives, Information Sciences, Volume 621, 2023, 708-728.

Crossrefs

Cf. A008793, A071095.

Programs

Mathematica

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}]

Formula

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).

a(n) = A008793(n+1) - A071095(n). - Vaclav Kotesovec, Nov 18 2023