R, 56 56 49 bytes
n=scan();x=2;for(i in 1:n){x=c(x,prod(x)+1)};cat(x[n+1]) Ungolfed:
n=scan() # Take input n x=2 # Initialize sequence to 2 for(i in 1:n){ x=c(x,prod(x)+1) # Append the product of the previous numbers + 1 } cat(x[n+1]) # Print the nth + 1 number in seq Slightly golfed thanks to @Frédéric:
n=scan();x=2;for(i in 1:n)x=c(x,prod(x)+1);x[n+1]