### Properties of a Composition of Exponential and Ordinary Generating Functions

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

L. Comtet, Advanced Combinatorics, D. Reidel Publishing Company (1974).

P. Flajolet and R. Sedgewick, Analytic Combinatorics, Cambridge University Press (2009).

R.L. Graham, D.E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley (1989).

K.-W. Hwang, D.V. Dolgy, D.S. Kim, T. Kim and S.H. Lee, Some theorems on Bernoulli and Euler numbers, Ars Combin. 109 (2013), 285 – 297.

N. Kilar and Y. Simsek, A new family of Fubini type numbers and polynomials associated with Apostol-Bernoulli numbers and polynomials, J. Korean Math. Soc. 54(5) (2017), 1605 – 1621.

M. Klazar, Bell numbers, their relatives, and algebraic differential equations, J. Combin. Theory Ser. A 102(1) (2003), 63 – 87.

D.V. Kruchinin and V.V. Kruchinin, A method for obtaining generating functions for central coefficients of triangles, J. Integer Seq. 15 (2012), 1 – 10.

D.V. Kruchinin and V.V. Kruchinin, Application of a composition of generating functions for obtaining explicit formulas of polynomials, J. Math. Anal. Appl. 404(1) (2013), 161 – 171.

V.V. Kruchinin and D.V. Kruchinin, Composita and its properties, Journal of Analysis and Number Theory 2 (2014), 37 – 44.

D.V. Kruchinin, Y.V. Shablya, O.O. Evsutin and A.A. Shelupanov, Integer properties of a composition of exponential generating functions, in Proc. Intl. Conf. of Numerical Analysis and Applied Mathematics, eds. T. Simos and C. Tsitouras, American Institute of Physics Inc., 2017, pp. 1–4.

P. Ribenboim, The Little Book of Bigger Primes, Springer-Verlag (2004).

A.M. Robert, A Course in p-adic Analysis, Springer (2000).

N.J.A. Sloane, The on-line encyclopedia of integer sequences, URL: http://oeis.org.

N.P. Smart, Cryptography Made Simple, Springer International Publishing (2016).

R.P. Stanley, Generating functions, in Studies in Combinatorics, ed. G.-C. Rota, Mathematical Association of America, 1978, pp. 100 – 141.

R.P. Stanley, Enumerative Combinatorics, Vol. 2, Cambridge University Press (1999).

H.S. Wilf, Generating Functionology, Academic Press, New York (1994).

S.Y. Yan, Primality Testing and Integer Factorization in Public-key Cryptography, Springer (2009).

DOI: http://dx.doi.org/10.26713%2Fcma.v9i4.1044

### Refbacks

- There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905