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Comptes Rendus. Mathématique
Combinatorics,  Mathematical Physics
A two-sided Faulhaber-like formula involving Bernoulli polynomials
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Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 41-44.

We give a new identity involving Bernoulli polynomials and combinatorial numbers. This provides, in particular, a Faulhaber-like formula for sums of the form 1 m (n-1) m +2 m (n-2) m ++(n-1) m 1 m for positive integers m and n.

Nous donnons une nouvelle identité utilisant les polynômes de Bernoulli et les coefficient binomiaux. Ceci fournit, en particulier, une formule de type Faulhaber pour des sommes de la forme 1 m (n-1) m +2 m (n-2) m ++(n-1) m 1 m m et n sont des entiers positifs.

Received : 2019-05-08
Revised : 2019-09-26
Accepted : 2020-01-21
Published online : 2020-03-19
DOI : https://doi.org/10.5802/crmath.10
@article{CRMATH_2020__358_1_41_0,
     author = {J. Fernando Barbero G. and Juan Margalef-Bentabol and Eduardo J.S. Villase\~nor},
     title = {A two-sided Faulhaber-like formula involving Bernoulli polynomials},
     journal = {Comptes Rendus. Math\'ematique},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {1},
     year = {2020},
     pages = {41-44},
     doi = {10.5802/crmath.10},
     language = {en},
     url={comptes-rendus.academie-sciences.fr/mathematique/item/CRMATH_2020__358_1_41_0/}
}
J. Fernando Barbero G.; Juan Margalef-Bentabol; Eduardo J.S. Villaseñor. A two-sided Faulhaber-like formula involving Bernoulli polynomials. Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 41-44. doi : 10.5802/crmath.10. https://comptes-rendus.academie-sciences.fr/mathematique/item/CRMATH_2020__358_1_41_0/

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