Journal of Integer Sequences, Vol. 17 (2014), Article 14.2.2

Bernoulli Numbers and a New Binomial Transform Identity

H. W. Gould
Department of Mathematics
West Virginia University
Morgantown, WV 26506

Jocelyn Quaintance
Department of Mathematics
Rutgers University
Piscataway, NJ 08854


Let (bn)n ≥ 0 be the binomial transform of (an)n ≥ 0. We show how a binomial transformation identity of Chen proves a symmetrical Bernoulli number identity attributed to Carlitz. We then modify Chen's identity to prove a new binomial transformation identity.

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(Concerned with sequences A027641 A027642.)

Received October 2 2013; revised version received January 3 2014. Published in Journal of Integer Sequences, January 3 2014.

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