Is it possible to solve this functional equation?

Question:Is it possible to solve this functional equation?

Posted: ComputerUser 535 Product: Maple 12

April 01 2021

F(n,n+1),2) = F(Product(x, k=1..n), 2)

how to solve function F?

Update

Above equation is wrong, below is newly updated

Expect F is product operator

F(2,3) + 2 = F(2,4)

F(3,4) + 3 = F(3,5)

solve([ F(1,2)+1=F(1,3), F(n,n+1) + n = F(n,n+2), F(n,n+1)= F(summation(k,k=1..n),2)],F) assuming n > 0

Expect F is new operator
solve([ F(1,2)*1=F(1,3), n*F(n,n+1) = F(n,n+2), F(n,n+1)= F(product(k,k=1..n),2)],F) assuming n > 0

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