Sum up the following series: $\sum^n_{k=1}\frac{k^2}{2^k}$

Question

How to find an explicit formula for the term $$\sum^n_{k=1}\frac{k^2}{2^k}$$ Then I discovered that
$$\sum^n_{k=1}\frac{k^2}{2^k}=1^22^n+2^22^{n-1}+3^22^{n-2}+\cdots+n^22^1-\frac{n(n+1)(2n+1)}{6}$$ But how to write $1^22^n+2^22^{n-1}+3^22^{n-2}+\cdots+n^22^1$ into explicit formula?? $$\\$$ A hint would be grateful.

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