Indecomposability of linear combinations of Bernoulli polynomials

In this manuscript, the authors prove the following: for an odd integer $n\geq 3$, and integers $a_n, a_{n-2}, a_{n-4},\ldots ,a_3,a_1$ such that $4\nmid a_n$, the polynomial $$ a_nB_n(x)+a_{n-2}B_{n-2}(x)+\cdots +a_3B_3(x)+a_1B_1(x), $$ where $B_n(x)$ stands for the $n$-th Bernoulli polynomial, is indecomposable over the field of complex numbers.