Geodesic
Some Properties of Generalized Euler Numbers
Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 606-617

Voir la notice de l'article provenant de la source Cambridge University Press

We define infinitely many sequences of integers one sequence for each positive integer k ≦ 2 by (1.1) where are the k-th roots of unity and (E(k))n is replaced by En(k) after multiplying out. An immediate consequence of (1.1) is (1.2) Therefore, we are interested in numbers of the form Esk (k) (s = 0, 1, 2, ...; k = 2, 3, ...).Some special cases have been considered in the literature. For k = 2, we obtain the Euler numbers (see e.g. [8]). The case k = 3 is considered briefly by D. H. Lehmer [7], and the case k = 4 by Leeming [6] and Carlitz ([1]and [2]). 
Leeming, D. J.; Macleod, R. A. Some Properties of Generalized Euler Numbers. Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 606-617. doi: 10.4153/CJM-1981-049-0
@article{10_4153_CJM_1981_049_0,
     author = {Leeming, D. J. and Macleod, R. A.},
     title = {Some {Properties} of {Generalized} {Euler} {Numbers}},
     journal = {Canadian journal of mathematics},
     pages = {606--617},
     year = {1981},
     volume = {33},
     number = {3},
     doi = {10.4153/CJM-1981-049-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-049-0/}
}
TY  - JOUR
AU  - Leeming, D. J.
AU  - Macleod, R. A.
TI  - Some Properties of Generalized Euler Numbers
JO  - Canadian journal of mathematics
PY  - 1981
SP  - 606
EP  - 617
VL  - 33
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-049-0/
DO  - 10.4153/CJM-1981-049-0
ID  - 10_4153_CJM_1981_049_0
ER  - 
%0 Journal Article
%A Leeming, D. J.
%A Macleod, R. A.
%T Some Properties of Generalized Euler Numbers
%J Canadian journal of mathematics
%D 1981
%P 606-617
%V 33
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-049-0/
%R 10.4153/CJM-1981-049-0
%F 10_4153_CJM_1981_049_0

[1] 1. Carlitz, L., Some arithmetic properties of a special sequence of integers, Can. Math. Bull. 19 (1976), 425–429. Google Scholar

[2] 2. Carlitz, L., Combinatorial property of a special polynomial sequence, Can. Math. Bull. 20 (1977), 183–188. Google Scholar

[3] 3. Carlitz, L., Permutations with prescribed pattern, Math. Nach. 58 (1973), 31–53. Google Scholar

[4] 4. Frobenius, F. G., Uber die Bernoulli schen Zahlen und die Eulerschen Polynôme, Gesammelte Abhandlungen III (Springer, Berlin-Heidelberg-New York, 1968), 440–478. Google Scholar

[5] 5. Gould, H. W., Combinatorial identities (Morgantown Printing and Binding Co., 1972). Google Scholar

[6] 6. Leeming, D. J., Some properties of a certain set of interpolating polynomials, Can. Math. Bull. 18 (1975), 529–537. Google Scholar

[7] 7. Lehmer, D. H., Lacunar y recurrence formulas for the numbers of Bernoulli and Euler, Ann. Math. 36 (1935), 637–649. Google Scholar

[8] 8. Norlund, N. E., Mémoire sur les polynômes de Bernoulli, Acta Math. 23 (1920), 121–144. Google Scholar

Cité par Sources :