The Zagier modification of Bernoulli numbers and a polynomial extension. Part I

Atul Dixit, Victor H. Moll, Christophe Vignat

The modified B_{n}^{*} = \sum_{r=0}^{n} \binom{n+r}{2r} \frac{B_{r}}{n+r}, \quad n > 0 introduced by D. Zagier in 1998 are extended to the polynomial case by replacing $B_r$ by t…