Existuje obecný vzorec pro součet mocnin přirozených čísel?

summary:The article derives the formula for the sum of the $k$-th powers of positive integers from $1$ to $n$ in the form of a polynomial in the variable $n$. The determination of the coefficients $a_{k,j}$ of the polynomial (a two-parametric problem) is converted into the determination of the members of a progression $B_p$k$, and Nikomachos theorem is mentioned as a special case