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

%I A321938 #23 Feb 12 2021 12:11:55
%S A321938 1,12,288,51840,2488320,209018880,75246796800,180592312320,
%T A321938 86684309913600,73557828698112000,86504006548979712000,
%U A321938 13494625021640835072000,9716130015581401251840000,23318712037395363004416000,559649088897488712105984000
%N A321938 Denominators of the Maclaurin coefficients of exp(1/x - 1/(exp(x)-1) - 1/2).
%C A321938 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).
%C A321938 The sequence is related to A001164 but differs from the 7th term.
%D A321938 L. J. Slater, Confluent Hypergeometric Functions, Cambridge University Press, 1960.
%H A321938 Richard P. Brent, M. L. Glasser, Anthony J. Guttmann, <a href="https://arxiv.org/abs/1812.00316">A Conjectured Integer Sequence Arising From the Exponential Integral</a>, arXiv:1812.00316 [math.NT], 2018.
%H A321938 N. M. Temme, <a href="http://campus.mst.edu/adsa/contents/v8n2p16.pdf">Remarks on Slater's asymptotic expansions of Kummer functions for large values of the a-parameter</a>, Adv. Dyn. Syst. Appl., 8 (2013), 365-377.
%e A321938 For n=0..3 the Maclaurin coefficients are 1, -1/12, 1/288, 67/61840.
%p A321938 A321938List := proc(len) local mu, ser;
%p A321938 mu  := h -> sum(bernoulli(2*k)/(2*k)!*h^(2*k-1), k=1..infinity);
%p A321938 ser := series(exp(mu(h)), h, len+2): seq(denom(coeff(ser,h,n)), n=0..len) end:
%p A321938 A321938List(14); # _Peter Luschny_, Dec 05 2018
%t A321938 Exp[1/x - 1/(Exp[x]-1) - 1/2] + O[x]^20 // CoefficientList[#, x]& // Denominator (* _Jean-François Alcover_, Jan 21 2019 *)
%o A321938 (PARI) x='x+O('x^25); apply(denominator, Vec(exp(1/x - 1/(exp(x)-1) - 1/2)))  \\ _Joerg Arndt_, Dec 05 2018
%Y A321938 Numerators are A321937.
%K A321938 nonn,frac
%O A321938 0,2
%A A321938 _Richard P. Brent_, Nov 22 2018