I. V. Blagouchine, and into the formal enveloping series with rational coefficients only, Journal of Number Theory, vol.158, pp.365-396, 2016.
DOI : 10.1016/j.jnt.2015.06.012

. [. Blagouchine, Two series expansions for the logarithm of the gamma function involving Stirling numbers, 2016.

]. L. Ca and . Carlitz, A note on Bernoulli and Euler polynomials of the second kind, Scripta Math, vol.25, pp.323-330, 1961.

M. [. Candelpergher and . Coppo, Le produit harmonique des suites, L'Ens. mathématique, pp.59-98, 2013.

M. [. Candelpergher and . Coppo, A new class of identities involving Cauchy numbers, harmonic numbers and zeta values, The Ramanujan Journal, vol.306, issue.3, pp.305-328, 2012.
DOI : 10.1007/s11139-011-9361-7

URL : https://hal.archives-ouvertes.fr/hal-00495767

H. [. Candelpergher, R. Gadiyar, and . Padma, Ramanujan summation and the exponential generating function $\sum_{k=0}^{\infty}\frac{z^{k}}{k!}\zeta^{\prime}(-k)$, The Ramanujan Journal, vol.99, issue.7, pp.99-122, 2010.
DOI : 10.1007/s11139-009-9166-0

. A. Db, K. Dil, and . Boyadzhiev, Euler sums of hyperharmonic numbers J. Number Theory, pp.490-498, 2015.

C. Jordan, Calculus of Finite Differences., Biometrika, vol.50, issue.1/2, 1965.
DOI : 10.2307/2333783

M. Kaneko and P. Numbers, Poly-Bernoulli numbers, Journal de Th??orie des Nombres de Bordeaux, vol.9, issue.1, pp.221-228, 1997.
DOI : 10.5802/jtnb.197

]. K. Ka and . Kamano, Dirichlet series associated with hyperharmonic numbers, Memoirs of the Osaka Institute of Technology, pp.11-15, 2011.

]. B. Ke and . Kellner, On quotients of Riemann zeta values at odd and even integer arguments, J. Number Theory, vol.133, pp.2684-2698, 2013.

[. Sun, Combinatorial identities in dual sequences, European Journal of Combinatorics, vol.24, issue.6, pp.709-718, 2003.
DOI : 10.1016/S0195-6698(03)00062-3

. [. Young, Rational series for multiple zeta and log gamma functions, Journal of Number Theory, vol.133, issue.12, pp.3995-4009, 2013.
DOI : 10.1016/j.jnt.2013.05.016

. [. Young, Symmetries of Bernoulli polynomial series and Arakawa???Kaneko zeta functions, Journal of Number Theory, vol.143, pp.142-161, 2014.
DOI : 10.1016/j.jnt.2014.02.025

. [. Young, The p-adic Arakawa???Kaneko zeta functions and p-adic Lerch transcendent, Journal of Number Theory, vol.155, pp.13-35, 2015.
DOI : 10.1016/j.jnt.2015.01.022