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Zbl 0863.11011
Dilcher, Karl
Sums of products of Bernoulli numbers. (English)
[J] J. Number Theory 60, No.1, 23-41 (1996). ISSN 0022-314X; ISSN 1096-1658/e

Closed expressions are obtained for sums of products of Bernoulli numbers of the form $$\sum {{2n} \choose {2j_1,\dots,2j_N}} B_{2j_1}\cdots B_{2j_N},$$ where the factor in parentheses is a multinomial coefficient and the summation is extended over all nonnegative integers $j_1,\dots,j_N$ whose sum is $n$. Corresponding results are derived for Bernoulli polynomials, and for Euler numbers and polynomials. Sums of this type were previously studied by Euler for $n=2$, and by others for $n=3$ and 4.
[T.M.Apostol (Pasadena)]

MSC 2000:: *11B68 Bernoulli numbers, etc.

Keywords: Euler polynomials; sums of products of Bernoulli numbers; Bernoulli polynomials; Euler numbers

Cited in: Zbl 0996.11017 Zbl 1042.11013 Zbl 0940.11009

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