Sums of Products of Bernoulli numbers of the second kind

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dc.creatorWu, Ming
dc.creatorPan, Hao
dc.date2007-09-19
dc.date.accessioned2026-07-07T08:30:47Z
dc.date.available2026-07-07T08:30:47Z
dc.descriptionThe 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}.
dc.descriptionAccepted by the Fibonacci Quarterly
dc.identifierhttps://arxiv.org/abs/0709.2947
dc.identifierhttp://arxiv.org/abs/0709.2947
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138330
dc.subjectNumber Theory
dc.subjectCombinatorics
dc.subject11B68; 05A19
dc.titleSums of Products of Bernoulli numbers of the second kind
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