Sums of Products of Bernoulli numbers of the second kind

Details Sums of Products of Bernoulli numbers of the second kind Sums of Products of Bernoulli numbers of the second kind

2007-09-19

arxiv.org/abs/0709.2947v1

Mathematics

Number Theory

Accepted by the Fibonacci Quarterly

Scientific paper

The Bernoulli numbers b_0,b_1,b_2,.... of the second kind are defined by
\sum_{n=0}^\infty b_nt^n=\frac{t}{\log(1+t)}. In this paper, we give an
explicit formula for the sum \sum_{j_1+j_2+...+j_N=n,
j_1,j_2,...,j_N>=0}b_{j_1}b_{j_2}...b_{j_N}. We also establish a q-analogue for
\sum_{k=0}^n b_kb_{n-k}=-(n-1)b_n-(n-2)b_{n-1}.

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