Poly-Bernoulli numbers
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Publication:1382103
DOI10.5802/jtnb.197zbMath0887.11011OpenAlexW2132672144WikidataQ57276099 ScholiaQ57276099MaRDI QIDQ1382103
Publication date: 25 March 1998
Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=JTNB_1997__9_1_221_0
congruencesStirling numbers of the second kindpoly-Bernoulli numberstheorem of Vandivervon Staudt-type theorem
Bell and Stirling numbers (11B73) Bernoulli and Euler numbers and polynomials (11B68) Congruences; primitive roots; residue systems (11A07)
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Cites Work
