No, it's not a homework problem, it's a random thing I was working on when playing around with algorithms to convert between music and systems of math.
I have these terms,
[MATH](1/1)x+(1/3)x^3+(1/15)x^5+(1/105)x^7+(1/945)x^9[/MATH]...
And I'm trying to come up with a formula to describe the coefficients in terms of a summation as part of a larger formula that I've already broken down. I've spent more than two hours testing different formulas and none of them work, but I know the concise pattern. If you want the nth coefficient, you'd do 1 divided by the derivative of the nth term times the coefficient (n-1)th term times the coefficient of the (n-2)nd term times the coefficient of the (n-3)rd term and so on. In a sense, it's like a factorial based off of derivatives, but I can't figure out a formula for it in terms of Sum(n=1) n->infinity. if n starts at 0, it's x^(2n-1), I got that down, I just can't figure out the coefficients, it's some kind of alternative factorial.