A321938 Denominators of the Maclaurin coefficients of exp(1/x - 1/(exp(x)-1) - 1/2).

1, 12, 288, 51840, 2488320, 209018880, 75246796800, 180592312320, 86684309913600, 73557828698112000, 86504006548979712000, 13494625021640835072000, 9716130015581401251840000, 23318712037395363004416000, 559649088897488712105984000

Offset

0,2

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).

The sequence is related to A001164 but differs from the 7th term.

References

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

Links

Table of n, a(n) for n=0..14.

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

A321938List := 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(denom(coeff(ser, h, n)), n=0..len) end:
A321938List(14); # Peter Luschny, Dec 05 2018

Mathematica

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

Prog

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

Crossrefs

Numerators are A321937.

Sequence in context: A159827 A192191 A145448 * A001164 A226100 A041267

Adjacent sequences: A321935 A321936 A321937 * A321939 A321940 A321941

Keyword

nonn,frac

Author

Richard P. Brent, Nov 22 2018

Status

approved