On new divisibility properties of generalized central trinomial coefficients and Legendre polynomials

Jovan Mikić

We present a new formula for the highest power of $a+b$ that divides the sum $B(n,m,a,b)={\sum }_{k=0}^n{\left(\genfrac{}{}{0ex}{}{n}{k}\right)}^m{a}^{n-k}{b}^k$ for the case $m=2$. By using this formula, we give…