The discussion revolves around finding the general term of a specific sequence: 0, 4, 22, 118, 718, 5038, 40318. The original poster provides the initial terms and seeks guidance on how to derive a general formula.
The discussion includes multiple participants exploring different interpretations and approaches. Some have suggested polynomial relationships and factorial connections, while others emphasize the importance of not providing direct answers to encourage the original poster's learning process.
There is mention of the need for a unique polynomial of degree 6 or less to fit the sequence, and some participants express concerns about the validity of proposed solutions. The original poster's attempts at finding a solution are acknowledged, but there is no consensus on the correct approach or final expression.
I'm not the original poster but still interested in solving this problem. Following your hint, the following is the expression I ended up with.phinds said:The next term is 362878. Doesn't seem very hard, I guess you just have to see the trick.
nmr said:I'm not the original poster but still interested in solving this problem. Following your hint, the following is the expression I ended up with.
A_n = A_(n-1) * (n+1) + 2(n+1)
How do I go about resolving A_(n-1) to a function/expression in terms of n?
phinds said:You have to take an assumed starting point, I think. I certainly did, but maybe someone with more math experience can give you an answer.
By the way, I obviously could have just posted the answer myself, but I thought I'd give the OP another shot at it, knowing that it isn't hard. I think you showed poor form in not doing the same.
The point of this forum is to help others figure things out, NOT to spoon feed them answers.