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%I #15 May 11 2018 01:42:08
%S 1,1,31,6721,5850271,15060446401,94396946822431,1258620297379341121,
%T 32323181593821704288671,1481630482369728860007652801,
%U 114129022540066183425609121804831
%N 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.
%H M. Domaratzki, <a href="http://research.cs.queensu.ca/TechReports/Reports/2001-449.pdf">A Generalization of the Genocchi Numbers with Applications to Enumeration of Finite Automata</a>, Technical Report 2001-449, Department of Computing and Information Science, Queen's University at Kingston (Kingston, Canada).
%H Michael Domaratzki, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL7/Domaratzki/doma23.html">Combinatorial Interpretations of a Generalization of the Genocchi Numbers</a>, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.6.
%H D. Dumont, <a href="http://dx.doi.org/10.1016/0012-365X(72)90039-8">Sur une conjecture de Gandhi concernant les nombres de Genocchi</a>, (in French), Discrete Mathematics 1 (1972) 321-327.
%H D. Dumont, <a href="http://dx.doi.org/10.1215/S0012-7094-74-04134-9">Interprétations combinatoires des nombres de Genocchi</a>, Duke Math. J., 41 (1974), 305-318.
%H D. Dumont, <a href="/A001469/a001469_3.pdf">Interprétations combinatoires des nombres de Genocchi</a>, Duke Math. J., 41 (1974), 305-318. (Annotated scanned copy)
%F a(n) = A(n-1, 1) for the above Gandhi polynomials.
%t a[n_ /; n >= 0, r_ /; r >= 0] := a[n, r] = r^5*a[n-1, r+1]-(r-1)^5*a[n-1, r]; a[1, r_ /; r >= 0] := r^5-(r-1)^5; a[_, _] = 1; a[n_] := a[n-1, 1]; Table[a[n], {n, 0, 10}] (* _Jean-François Alcover_, May 23 2013 *)
%Y Cf. A001469, A065755, A065757, A064624, A064625.
%K easy,nonn
%O 1,3
%A Mike Domaratzki (mdomaratzki(AT)alumni.uwaterloo.ca), Nov 17 2001
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