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A222804
Denominators of coefficients in asymptotic expansion of log z + psi(z+1/z), where psi is the digamma function.
3
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
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
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Mar 10 2013
EXTENSIONS
More terms from Alois P. Heinz, Mar 13 2013
STATUS
approved