Combinatorial Interpretations of a Generalization of the Genocchi Numbers

We consider a natural generalization of the well-studied Genocchi numbers flrst proposed by Han. This generalization proves useful in enumerating the class of deterministic flnite automata (DFA) that accept a flnite language, and in enumerating a generalization of permutations counted by Dumont.

[1]  John Riordan,et al.  The divided central differences of zero , 1963 .

[2]  Gunter Bach.  Über eine Verallgemeinerung der Differenzengleichung der Stirlingschen Zahlen 2. Art und einige damit zusammenhängende Fragen. , 1968 .

[3]  D. Foata,et al.  Theorie Geometrique des Polynomes Euleriens , 1970 .

[4]  J. M. Gandhi,et al.  A Conjectured Representation of Genocchi Numbers , 1970 .

[5]  Dominique Dumont.  Sur une conjecture de Gandhi concernant les nombres de Genocchi , 1972, Discret. Math..

[6]  John Riordan,et al.  Proof of a conjecture on Genocchi numbers , 1973, Discrete Mathematics.

[7]  Dominique Dumont,et al.  Interprétations combinatoires des nombres de Genocchi , 1974 .

[8]  Dominique Dumont,et al.  Une propriété de symétrie des nombres de Genocchi , 1976 .

[9]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[10]  Gérard Viennot,et al.  A Combinatorial Interpretation of the Seidel Generation of Genocchi Numbers , 1980 .

[11]  M. W. Shields.  An Introduction to Automata Theory , 1988 .

[12]  Dominique Dumont,et al.  Dérangements et nombres de Genocchi , 1994, Discret. Math..

[13]  N. J. A. Sloane,et al.  The On-Line Encyclopedia of Integer Sequences , 2003, Electron. J. Comb..

[14]  D. Dumont,et al.  Derangements and Genocchi numbers , 1994 .

[15]  Sheng Yu.  Regular Languages , 1997, Handbook of Formal Languages.

[16]  Jeffrey Shallit,et al.  On the Number of Distinct Languages Accepted by Finite Automata with n States , 2002, DCFS.