A special class of Bell polynomials

Author:
F. T. Howard

Journal:
Math. Comp. **35** (1980), 977-989

MSC:
Primary 10A40; Secondary 05A15

MathSciNet review:
572870

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Abstract | References | Similar Articles | Additional Information

Abstract: We examine the integers defined by means of

**[1]**L. Carlitz,*Eulerian numbers and polynomials*, Math. Mag.**32**(1958/1959), 247–260. MR**0104845****[2]**Louis Comtet,*Advanced combinatorics*, Revised and enlarged edition, D. Reidel Publishing Co., Dordrecht, 1974. The art of finite and infinite expansions. MR**0460128****[3]**F. T. Howard,*A sequence of numbers related to the exponential function*, Duke Math. J.**34**(1967), 599–615. MR**0217035****[4]**F. T. Howard,*Associated Stirling numbers*, Fibonacci Quart.**18**(1980), no. 4, 303–315. MR**600368****[5]**F. T. Howard,*Bell polynomials and degenerate Stirling numbers*, Rend. Sem. Mat. Univ. Padova**61**(1979), 203–219 (1980). MR**569660****[6]**F. T. Howard,*Numbers generated by the reciprocal of 𝑒^{𝑥}-𝑥-1*, Math. Comp.**31**(1977), no. 138, 581–598. MR**0439741**, 10.1090/S0025-5718-1977-0439741-4**[7]**F. T. Howard,*Polynomials related to the Bessel functions*, Trans. Amer. Math. Soc.**210**(1975), 233–248. MR**0379348**, 10.1090/S0002-9947-1975-0379348-5**[8]**F. T. Howard,*Properties of the van der Pol numbers and polynomials*, J. Reine Angew. Math.**260**(1973), 35–46. MR**0318054****[9]**F. T. Howard,*The van der Pol numbers and a related sequence of rational numbers.*, Math. Nachr.**42**(1969), 89–102. MR**0258739****[10]**C. JORDAN,*Calculus of Finite Differences*, Chelsea, New York, 1950.**[11]**John Riordan,*An introduction to combinatorial analysis*, Wiley Publications in Mathematical Statistics, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR**0096594**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1980-0572870-3

Keywords:
Exponential partial Bell polynomial,
Stirling number of the second kind,
associated Stirling number of the second kind,
Bernoulli number,
Genocchi number,
van der Pol number

Article copyright:
© Copyright 1980
American Mathematical Society