A special class of Bell polynomials
Author:
F. T. Howard
Journal:
Math. Comp. 35 (1980), 977989
MSC:
Primary 10A40; Secondary 05A15
MathSciNet review:
572870
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Abstract: We examine the integers defined by means of and, in particular, we show how these integers are related to the Bernoulli, Genocchi and van der Pol numbers, and the numbers generated by the reciprocal of . We prove that the are also related to the numbers defined by in much the same way the associated Stirling numbers are related to the Stirling numbers. Finally, we examine, more generally, the Bell polynomials and show how the methods of this paper can be used to prove several formulas involving the Bernoulli and Stirling numbers.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198005728703
PII:
S 00255718(1980)05728703
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
