Question 33
Let $f:\mathbb N\to\mathbb Q$, where $\mathbb N$ is the set of natural numbers and $\mathbb Q$ is the set of rational numbers. Suppose $f(1)=\dfrac32$ and
$$f(x+y)=\left(1+\frac y{x+1}\right)f(x)+\left(1+\frac x{y+1}\right)f(y)+x^2y+xy+xy^2$$
for all natural numbers $x,y$. Find $f(20)$.
$$f(x+y)=\left(1+\frac y{x+1}\right)f(x)+\left(1+\frac x{y+1}\right)f(y)+x^2y+xy+xy^2$$
for all natural numbers $x,y$. Find $f(20)$.