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- F. T. Howard
- Discrete Mathematics
- 1985

- F. T. Howard
- 1994

In particular, B^\0) = B^\ the Bernoulli number of order k, and BJp = Bn, the ordinary Bernoulli number. Note also that B^ = 0 for n > 0. The polynomials B^\z) and the numbers B^ were first defined and studied by Niels Norlund in the 1920s; later they were the subject of many papers by L. Carlitz and others. For the past twenty-five years not much has been… (More)

- F. T. Howard
- Discrete Mathematics
- 1982

We define the potential polynomial Fjjz’ and the exponential Bell polynomial B,, (0, . . . , 0, fP fr+,* * . . ) and we prove a theorem relating the two. Though not well-known, the theorem has many applications, some of which we discuss in this paper. fn particular, the theorem provides a systematic approach to a number of formulas and identities involving… (More)

- Mehmet Cenkci, F. T. Howard
- Discrete Mathematics
- 2007

- F. T. Howard
- Discrete Mathematics
- 1996

- By F. T. Howard, F. T. HOWARD
- 2010

and we prove similar equations involving the Bernoulli numbers, the van der Pol numbers, and the numbers generated by the reciprocal of ex x 1. (All of these special numbers are defined in Section 2.) Thus, the V(n, k) provide a link between these special numbers which is not obvious. In Section 5 we look, more generally, at the Bell polynomials 'n,fc(ai>… (More)

- FRED T. HOWARD
- 2006

We give a new simple proof of Chizhong Zhou’s method of constructing identities for linear recurrence sequences. We show how Zhou’s theorem can be used to prove a wide variety of identities for generalized Fibonacci and Tribonacci numbers.

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