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\lfloor {\frac {n}{2}}\right\rfloor }{\frac {1}{4^{k}\cdot (k!)^{2}\cdot (n-2k)!}},\quad n\geq 1}
