A note on sums of products of Bernoulli numbers (Q607148)

Let \((B_n)\) be the Bernoulli numbers. The author presents an explicit formula for the sum \[ \sum_{r_1,\dots,r_n\geq 0\atop r_1+\dots+r_n=r}\binom{2r}{2r_1,\dots,2r_n}B_{2r_1}\dots B_{2r_n}, \] where \(\binom{2r}{2r_1,\dots,2r_n}\) are the multinomial coefficients.