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A227540 Denominator of the rationals obtained from the e.g.f. D(1,x), a Debye function. 1


%S 1,4,18,1,150,1,294,1,270,1,726,1,35490,1,90,1,8670,1,15162,1,6930,1,

%T 3174,1,68250,1,162,1,25230,1,443982,1,16830,1,210,1,71010030,1,234,1,

%U 554730,1,77658,1,31050,1,13254,1,2274090,1,3366,1,84270,1,43890,1

%N Denominator of the rationals obtained from the e.g.f. D(1,x), a Debye function.

%C The numerator sequence seems to be the one of the Bernoulli numbers A027641.

%C D(1,x) := (1/x)*int(t/(exp(t)-1),t=0..x) which is (1/x)times the Debye function of the Abramowitz-Stegun link for n=1, is the e.g.f. for {B(k)/(k+1)}, k=0..infinity, with the Bernoulli numbers B(k) = A027641(k)/A027642(k). This follows after using the e.g.f. t/(exp(t)-1) of {B(k)} and integrating term by term (allowed for |x| <= r < rho for some small enough rho).

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, pp. 998, equ. 27.1.1 for n=1, with an extra factor 1/x.

%F a(n) = denominator(B(n)/(n+1)) (in lowest terms), n >= 0. See the comment on the e.g.f. D(1,x) above.

%Y Cf. A027641/A027642 (Bernoulli), A120082/A120083 for the rationals B(n)/(n+1)!.

%K nonn,easy,frac

%O 0,2

%A _Wolfdieter Lang_, Jul 15 2013

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