A065756 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.

1, 1, 31, 6721, 5850271, 15060446401, 94396946822431, 1258620297379341121, 32323181593821704288671, 1481630482369728860007652801, 114129022540066183425609121804831

Offset

1,3

Links

Table of n, a(n) for n=1..11.

M. Domaratzki, A Generalization of the Genocchi Numbers with Applications to Enumeration of Finite Automata, Technical Report 2001-449, Department of Computing and Information Science, Queen's University at Kingston (Kingston, Canada).

Michael Domaratzki, Combinatorial Interpretations of a Generalization of the Genocchi Numbers, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.6.

D. Dumont, Sur une conjecture de Gandhi concernant les nombres de Genocchi, (in French), Discrete Mathematics 1 (1972) 321-327.

D. Dumont, Interprétations combinatoires des nombres de Genocchi, Duke Math. J., 41 (1974), 305-318.

D. Dumont, Interprétations combinatoires des nombres de Genocchi, Duke Math. J., 41 (1974), 305-318. (Annotated scanned copy)

Formula

a(n) = A(n-1, 1) for the above Gandhi polynomials.

Mathematica

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 *)

Crossrefs

Cf. A001469, A065755, A065757, A064624, A064625.

Sequence in context: A245290 A090681 A297767 * A263378 A306840 A212858

Adjacent sequences: A065753 A065754 A065755 * A065757 A065758 A065759

Keyword

easy,nonn

Author

Mike Domaratzki (mdomaratzki(AT)alumni.uwaterloo.ca), Nov 17 2001

Status

approved