Domaratzki, Michael Combinatorial interpretations of a generalization of the Genocchi numbers. (English) Zbl 1092.11010 J. Integer Seq. 7, No. 3, Art. 04.3.6, 11 p. (2004). The author studies a generalization of Genocchi numbers that was proposed by G. Han [Sémin. Lothar. Comb. 24, B24a (1990; Zbl 0981.05516)]. These numbers give a bound for the number of deterministic finite automata that accept a given finite language. They are also linked to counting some sets of permutations. Reviewer: Jean-Paul Allouche (Orsay) Cited in 1 ReviewCited in 14 Documents MSC: 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 05A05 Permutations, words, matrices 68Q45 Formal languages and automata 11B65 Binomial coefficients; factorials; \(q\)-identities Keywords:Genocchi numbers; Gandhi polynomials; finite languages; finite deterministic automata; enumeration of permutations Citations:Zbl 0981.05516 Software:OEIS PDFBibTeX XMLCite \textit{M. Domaratzki}, J. Integer Seq. 7, No. 3, Art. 04.3.6, 11 p. (2004; Zbl 1092.11010) Full Text: EuDML EMIS Online Encyclopedia of Integer Sequences: Genocchi numbers (of first kind); unsigned coefficients give expansion of x*tan(x/2). Generalization of the Genocchi numbers given by the Gandhi polynomials A(n+1,r) = r^3 A(n, r + 1) - (r - 1)^3 A(n, r); A(1,r) = r^3 - (r-1)^3. Generalization of the Genocchi numbers. Generated by the Gandhi polynomials A(n+1,r) = r^4 A(n,r+1) - (r-1)^4 A(n,r); A(1,r) = r^4 - (r-1)^4. Triangle of Gandhi polynomial coefficients. Triangle of Gandhi polynomial coefficients. Second column of A065747. Second column of A065748. Triangle of Gandhi polynomial coefficients. Generalization of the Genocchi numbers given by the Gandhi polynomials A(n+1,r) = r^5 A(n, r + 1) - (r - 1)^5 A(n, r); A(1,r) = r^5 - (r-1)^5. Second column of A065755.