27020 (Gheorghe Szöllösy)
Să se calculeze suma ∑ k = 0 [ n 2 ] [ 1 4 k ⋅ ( k ! ) 2 ( n − 2 k ) ! ] , n ≥ 1 {\displaystyle \sum _{k=0}^{\left[{\frac {n}{2}}\right]}\left[{\dfrac {1}{4^{k}\cdot (k!)^{2}(n-2k)!}}\right],n\geq 1}
![{\displaystyle \sum _{k=0}^{\left[{\frac {n}{2}}\right]}\left[{\dfrac {1}{4^{k}\cdot (k!)^{2}(n-2k)!}}\right],n\geq 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ebeedf567bf6522a8c4354b20722e9e9eef1c114)
