A note on sums of products of Bernoulli numbers. (English) Zbl 1222.11031

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.


11B68 Bernoulli and Euler numbers and polynomials
11B65 Binomial coefficients; factorials; \(q\)-identities
Full Text: DOI


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