A222804 Denominators of coefficients in asymptotic expansion of log z + psi(z+1/z), where psi is the digamma function.

1, 2, 12, 2, 40, 2, 630, 2, 560, 2, 132, 2, 6006, 2, 156, 2, 19040, 2, 610470, 2, 41800, 2, 276, 2, 39468, 2, 12, 2, 15080, 2, 31150350, 2, 1180480, 2, 12, 2, 215333118, 2, 444, 2, 23993200, 2, 101072790, 2, 39560, 2, 564, 2, 63069864, 2, 132, 2, 2120, 2

Offset

0,2

References

Mohammad K. Azarian, Problem 1218, Pi Mu Epsilon Journal, Vol. 13, No. 2, Spring 2010, p. 116. Solution published in Vol. 13, No. 3, Fall 2010, pp. 183-185.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

M. W. Coffey, V. de Angelis, A. Dixit, V. H. Moll, et al., The Zagier polynomials. Part II: Arithmetic properties of coefficients, 2013

Example

0, -1/2, 11/12, 1/2, -13/40, -1/2, 29/630, 1/2, 109/560, -1/2, -67/132, 1/2, 6571/6006, ...

Mathematica

s = Series[Log[z] + PolyGamma[z+1/z], {z, Infinity, 53}] // Normal; CoefficientList[s + 2*Log[1/z], 1/z] // Denominator (* Jean-François Alcover, Mar 07 2014 *)

Crossrefs

Cf. A222803-A222806.

Sequence in context: A263631 A010239 A320975 * A128268 A185633 A246737

Adjacent sequences: A222801 A222802 A222803 * A222805 A222806 A222807

Keyword

nonn,frac

Author

N. J. A. Sloane, Mar 10 2013

Extensions

More terms from Alois P. Heinz, Mar 13 2013

Status

approved