A222803 Numerators of coefficients in asymptotic expansion of log z + psi(z+1/z), where psi is the digamma function.

0, -1, 11, 1, -13, -1, 29, 1, 109, -1, -67, 1, 6571, -1, -415, 1, 162573, -1, -23663513, 1, 10230003, -1, -564409, 1, 854671223, -1, -3380281, 1, 66346781597, -1, -2525207721201139, 1, 2050779017959603, -1, -513555084749, 1, 258395660795799074117, -1

Offset

0,3

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, 37}] // Normal; CoefficientList[s + 2*Log[1/z], 1/z] // Numerator (* Jean-François Alcover, Mar 07 2014 *)

Crossrefs

Cf. A222804-A222806.

Sequence in context: A279247 A281096 A280506 * A201132 A212488 A373821

Adjacent sequences: A222800 A222801 A222802 * A222804 A222805 A222806

Keyword

sign,frac

Author

N. J. A. Sloane, Mar 10 2013

Extensions

More terms from Alois P. Heinz, Mar 13 2013

Status

approved