Sequence for a conjecture

[prime bronze]

Help with this please

[lusty trail]

$dy/dt=a(1+at)^{-1} $ and $d^2y/dt^2= -a^2(1+at)^{-2}$ and $d^3y/dt^3=2a^3(1+at)^{-3}$ and $d^4y/dt^4=2\cdot (-3)a^4(1+at)^{-4}$ differentiating n times you get $d^ny/dt^n=(-1)^{n-1}(n-1)!a^{n}(1+at)^{-n}$