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11: 24.16 Generalizations
24.16.8 β n ( λ ) = n ! b n λ n + k = 1 n / 2 n 2 k B 2 k s ( n 1 , 2 k 1 ) λ n 2 k , n = 2 , 3 , .
Here s ( n , m ) again denotes the Stirling number of the first kind. …
12: 26.15 Permutations: Matrix Notation
13: Bibliography J
  • D. J. Jeffrey and N. Murdoch (2017) Stirling Numbers, Lambert W and the Gamma Function. In Mathematical Aspects of Computer and Information Sciences, J. Blömer, I. S. Kotsireas, T. Kutsia, and D. E. Simos (Eds.), Cham, pp. 275–279.
  • 14: Bibliography G
  • K. Goldberg, F. T. Leighton, M. Newman, and S. L. Zuckerman (1976) Tables of binomial coefficients and Stirling numbers. J. Res. Nat. Bur. Standards Sect. B 80B (1), pp. 99–171.
  • H. W. Gould (1960) Stirling number representation problems. Proc. Amer. Math. Soc. 11 (3), pp. 447–451.
  • 15: Bibliography T
  • N. M. Temme (1993) Asymptotic estimates of Stirling numbers. Stud. Appl. Math. 89 (3), pp. 233–243.
  • 16: 8.11 Asymptotic Approximations and Expansions
    This reference also contains explicit formulas for b k ( λ ) in terms of Stirling numbers and for the case λ > 1 an asymptotic expansion for b k ( λ ) as k . … This reference also contains explicit formulas for the coefficients in terms of Stirling numbers. …
    17: Bibliography M
  • L. Moser and M. Wyman (1958a) Asymptotic development of the Stirling numbers of the first kind. J. London Math. Soc. 33, pp. 133–146.
  • L. Moser and M. Wyman (1958b) Stirling numbers of the second kind. Duke Math. J. 25 (1), pp. 29–43.
  • 18: 5.11 Asymptotic Expansions
    For explicit formulas for g k in terms of Stirling numbers see Nemes (2013a), and for asymptotic expansions of g k as k see Boyd (1994) and Nemes (2015a). …
    19: Errata
  • Table 26.8.1

    Originally the Stirling number s ( 10 , 6 ) was given incorrectly as 6327. The correct number is 63273.

    n k
    0 1 2 3 4 5 6 7 8 9 10
    10 0 3 62880 10 26576 11 72700 7 23680 2 69325 63273 9450 870 45 1

    Reported 2013-11-25 by Svante Janson.

  • 20: Bibliography B
  • W. E. Bleick and P. C. C. Wang (1974) Asymptotics of Stirling numbers of the second kind. Proc. Amer. Math. Soc. 42 (2), pp. 575–580.