Factor independent term from a summation?

Can I factor $$t^2$$ from $$\frac{1}{t}\sum_{n=1}^{n1}t^2Exp[-a n^2+bn]$$ to get

$$t\sum_{n=1}^{n1}Exp[-a n^2+bn]$$ using some command?

1/t Sum[t^2 Exp[-a n^2 + b n], {n, 1, n1}]