%I #8 Dec 01 2023 05:16:37

%S 1,2,10,80,1008,19764,600028,28134464,2034669118,226781039624

%N Number of commutative discrete aggregation functions defined on the finite chain L_n={0,1,...,n-1,n} that are smooth.

%C The number of smooth and commutative discrete aggregation functions on the finite chain L_n={0,1,...,n-1,n}, i.e., the number of monotonic increasing binary functions F: L_n^2->L_n such that F(0,0)=0 and F(n,n)=n, F(x,y)=F(y,x) for all x,y in L_n (commutativity), and F(x+1,y)-F(x,y)<=1 and F(y,x+1)-F(y,x)<=1 for all y in L_n and x in L_n\{n} (smooth).

%C Also, the number of (n+1)X(n+1) integer symmetric matrices (m_{i,j}) such that m_{1,1}=1, m_{n+1,n+1}=n+1, and all rows and columns are (weakly) monotonic without jumps larger than 1.

%Y Symmetric counterpart of matrices enumerated in A306372.

%Y Smooth counterpart of operators defined in A366447.

%K nonn,hard,more

%O 0,2

%A _Marc Munar_, Nov 18 2023

%E a(0) and a(7)-a(9) from _Martin Ehrenstein_, Dec 01 2023