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Computation of Euler’s type sums of the products of Bernoulli numbers. (English) Zbl 1228.11025

Summary: In this work, the authors present several formulas which compute the following Euler type and Dilcher type sums of the products of Bernoulli numbers B n :

Ω n (m) := j 1 ++j m =n(j 1 ,,j m 1) 2n2j 1 ,,2j m B 2j 1 B 2j m

and

Δ n (m) := j 1 ++j m =n(j 1 ,,j m 0) 2n2j 1 ,,2j m B 2j 1 B 2j m

respectively, where

nk 1 ,,k m =n! k 1 !k m !

denotes, as usual, the multinomial coefficient.


MSC:
11B68Bernoulli and Euler numbers and polynomials
Software:
OEIS
References:
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