Abramson, M. and Moser, W. O. J. "Permutations without Rising or Falling -Sequences." Ann. Math. Statist.38, 1245-1254, 1967.André, D. "Mémoir sur les couples actifs de permutations." Mem. della Pontificia Acad. Romana dei Nuovo Lincei23, 189-223, 1906.Carlitz, L. "Note on a Paper of Shanks." Amer. Math. Monthly59, 239-241, 1952.Carlitz, L. "Eulerian Numbers and Polynomials." Math. Mag.32, 247-260, 1959.Carlitz, L. "Eulerian Numbers and Polynomials of Higher Order." Duke Math. J.27, 401-423, 1960.Carlitz, L. "A Note on the Eulerian Numbers." Arch. Math.14, 383-390, 1963.Carlitz, L. and Riordan, J. "Congruences for Eulerian Numbers." Duke Math. J.20, 339-343, 1953.Carlitz, L.; Roselle, D. P.; and Scoville, R. "Permutations and Sequences with Repetitions by Number of Increase." J. Combin. Th.1, 350-374, 1966.Cesàro, E. "Dérivées des fonctions de fonctions." Nouv. Ann.5, 305-327, 1886.Comtet, L. "Permutations by Number of Rises; Eulerian Numbers." §6.5 in Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. 多德雷赫特，荷蘭: Reidel, pp. 51 and 240-246, 1974.David, F. N.; Kendall, M. G.; and Barton, D. E. Symmetric Function and Allied Tables. 劍橋，英國: 劍橋大學出版社, p. 260, 1966.Dillon, J. F.; Roselle, D. P. "Eulerian Numbers of Higher Order." Duke Math. J.35, 247-256, 1968.Foata, D. and Schützenberger, M.-P. Théorie géométrique des polynômes Eulériens. 柏林: Springer-Verlag, 1970.Frobenius, F. G. "Ueber die Bernoullischen Zahlen und die Eulerischen Polynome." Sitzungsber. Preuss. Akad. Wiss., pp. 808-847, 1910.Graham, R. L.; Knuth, D. E.; and Patashnik, O. "Eulerian Numbers." §6.2 in Concrete Mathematics: A Foundation for Computer Science, 2nd ed. 雷丁，馬薩諸塞州: Addison-Wesley, pp. 267-272, 1994.Kimber, A. C. "Eulerian Numbers." Supplement to Encyclopedia of Statistical Sciences. (Ed. S. Kotz, N. L. Johnson, and C. B. Read). 紐約: Wiley, pp. 59-60, 1989.Poussin, F. "Sur une propriété arithmétique de certains polynomes associés aux nombres d'Euler." C. R. Acad. Sci. Paris Sér. A-B266, A392-A393, 1968.Salama, I. A. and Kupper, L. L. "A Geometric Interpretation for the Eulerian Numbers." Amer. Math. Monthly93, 51-52, 1986.Schrutka, L. "Eine neue Einleitung der Permutationen." Math. Ann.118, 246-250, 1941.Shanks, E. B. "Iterated Sums of Powers of the Binomial Coefficients." Amer. Math. Monthly58, 404-407, 1951.Sloane, N. J. A. 序列 A000295/M3416, A000460/M4795, A000498/M5188, 和 A008292，出自 "The On-Line Encyclopedia of Integer Sequences."Tomić, M. "Sur une nouvelle classe de polynômes de la théorie des fonctions spéciales." Publ. Fac. Elect. U. Belgrade, No. 38, 1960.Toscano, L. "Su due sviluppi della potenza di un binomio, -coefficienti di Eulero." Bull. S. M. Calabrese16, 1-8, 1965.
給出了集合 
中恰好有 
個 排列升序 的排列數（Graham et al. 1994, p. 267）。請注意，Comtet (1974) 使用了略有不同的尤拉數定義，他將尤拉數 
(有時也表示為 
) 定義為長度為 
的 排列遊程 的數量，因此 
。
是 多對數函式。因此，
由 
在以下表達式中的係數給出
具有 指數生成函式
滿足 遞推關係
, 
, 
, ...
排列成三角形，得到 尤拉數三角形
-Sequences." Ann. Math. Statist. 38, 1245-1254, 1967.André, D. "Mémoir sur les couples actifs de permutations." Mem. della Pontificia Acad. Romana dei Nuovo Lincei 23, 189-223, 1906.Carlitz, L. "Note on a Paper of Shanks." Amer. Math. Monthly 59, 239-241, 1952.Carlitz, L. "Eulerian Numbers and Polynomials." Math. Mag. 32, 247-260, 1959.Carlitz, L. "Eulerian Numbers and Polynomials of Higher Order." Duke Math. J. 27, 401-423, 1960.Carlitz, L. "A Note on the Eulerian Numbers." Arch. Math. 14, 383-390, 1963.Carlitz, L. and Riordan, J. "Congruences for Eulerian Numbers." Duke Math. J. 20, 339-343, 1953.Carlitz, L.; Roselle, D. P.; and Scoville, R. "Permutations and Sequences with Repetitions by Number of Increase." J. Combin. Th. 1, 350-374, 1966.Cesàro, E. "Dérivées des fonctions de fonctions." Nouv. Ann. 5, 305-327, 1886.Comtet, L. "Permutations by Number of Rises; Eulerian Numbers." §6.5 in 
-coefficienti di Eulero." Bull. S. M. Calabrese 16, 1-8, 1965.