A special class of Bell polynomials

Author:
F. T. Howard

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

MSC:
Primary 10A40; Secondary 05A15

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

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.*, v. 33, 1959, pp. 247-260. MR**0104845 (21:3596)****[2]**L. COMTET,*Advanced Combinatorics*, Reidel, Dordrecht and Boston, Mass., 1974. MR**0460128 (57:124)****[3]**F. T. HOWARD, "A sequence of numbers related to the exponential function,"*Duke Math. J.*, v. 34, 1967, pp. 599-616. MR**0217035 (36:130)****[4]**F. T. HOWARD, "Associated Stirling numbers,"*Fibonacci Quart*. (To appear.) MR**600368 (82e:05023)****[5]**F. T. HOWARD, "Bell polynomials and degenerate Stirling numbers,"*Rend. Sem. Mat. Padova.*(To appear.) MR**569660 (81g:10027)****[6]**F. T. HOWARD, "Numbers generated by the reciprocal of ,"*Math. Comp.*, v. 31, 1977, pp. 581-598. MR**0439741 (55:12627)****[7]**F. T. HOWARD, "Polynomials related to the Bessel functions,"*Trans. Amer. Math. Soc.*, v. 210, 1975, pp. 233-248. MR**0379348 (52:253)****[8]**F. T. HOWARD, "Properties of the van der Pol numbers and polynomials,"*J. Reine Angew. Math.*, v. 260, 1973, pp. 35-46. MR**0318054 (47:6603)****[9]**F. T. HOWARD, "The van der Pol numbers and a related sequence of rational numbers,"*Math. Nachr.*, v. 42, 1969, pp. 80-102. MR**0258739 (41:3385)****[10]**C. JORDAN,*Calculus of Finite Differences*, Chelsea, New York, 1950.**[11]**J. RIORDAN,*An Introduction to Combinatorial Analysis*, Wiley, New York, 1958. MR**0096594 (20:3077)**

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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