Answer:
The pattern is this: I create a function p(x) such that
p(1)=1
p(2)=1
p(3)=3
p(4)=4
p(5)=6
p(6)=7
p(7)=9
Therefore, trivially evaluating at x=8 gives:
p(8)= 420+(cos(15))^3 -(arccsc(0.304))^(e^56) + zeta(2)
Ok, I know this isn’t what you were looking for. Be careful, you must specify what type of pattern is needed, because the above satisfies the given constraints.
Explanation: