Solving the recurrence relation $T(n) = (n+1)/n*T(n-1) + c(2n-1)/n, T(1) = 0$

Question

I tried a lot of different methods. Not able to make out the series. Could anyone help me i this regard?

$ T(n) = \frac{(n+1)}{n}T(n-1) + c\frac{(2n-1)}{n} , T(1) = 0 $

Answer 1

$$\frac{T(n)}{n+1}=\frac{T(n-1)}{n}+c\frac{2n-1}{n(n+1)}=\frac{T(n-1)}{n}+\frac{3c}{n+1}-\frac{c}n$$