A321937 Numerators of the Maclaurin coefficients of exp(1/x - 1/(exp(x)-1) - 1/2).

1, -1, 1, 67, -283, -5911, 269891, 114551, -9390523, -1021798901, 273468378049, 3918564638257, -872697935308349, -131115162268691, 1397912875942181, 2172284899403876321, -3926446823184958835813, -284746035618826337921, 286113629384558337084185927

Offset

0,4

Comments

The Maclaurin coefficients arise in a theorem of Slater (1960) on asymptotic expansions of confluent hypergeometric functions, see Sec. 3.1 of the paper by Temme (2013), and Theorem 5 of the preprint by Brent et al. (2018).

References

L. J. Slater, Confluent Hypergeometric Functions, Cambridge University Press, 1960.

Links

Table of n, a(n) for n=0..18.

Richard P. Brent, M. L. Glasser, Anthony J. Guttmann, A Conjectured Integer Sequence Arising From the Exponential Integral, arXiv:1812.00316 [math.NT], 2018.

N. M. Temme, Remarks on Slater's asymptotic expansions of Kummer functions for large values of the a-parameter, Adv. Dyn. Syst. Appl., 8 (2013), 365-377.

Example

For n=0..3 the Maclaurin coefficients are 1, -1/12, 1/288, 67/61840.

Maple

A321937List := proc(len) local mu, ser;
mu  := h -> sum(bernoulli(2*k)/(2*k)!*h^(2*k-1), k=1..infinity);
ser := series(exp(mu(-h)), h, len+2): seq(numer(coeff(ser, h, n)), n=0..len) end:
A321937List(18); # Peter Luschny, Dec 05 2018

Mathematica

Exp[1/x - 1/(Exp[x]-1) - 1/2] + O[x]^20 // CoefficientList[#, x]& // Numerator (* Jean-François Alcover, Jan 21 2019 *)

Prog

(PARI) x='x+O('x^25); apply(numerator , Vec(exp(1/x - 1/(exp(x)-1) - 1/2))) \\ Joerg Arndt, Dec 05 2018

Crossrefs

Denominators are A321938.

Sequence in context: A140731 A140855 A052164 * A270615 A142804 A033242

Adjacent sequences: A321934 A321935 A321936 * A321938 A321939 A321940

Keyword

sign,frac

Author

Richard P. Brent, Nov 22 2018

Status

approved