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

1, 4, 18, 1, 150, 1, 294, 1, 270, 1, 726, 1, 35490, 1, 90, 1, 8670, 1, 15162, 1, 6930, 1, 3174, 1, 68250, 1, 162, 1, 25230, 1, 443982, 1, 16830, 1, 210, 1, 71010030, 1, 234, 1, 554730, 1, 77658, 1, 31050, 1, 13254, 1, 2274090, 1, 3366, 1, 84270, 1, 43890, 1

Offset: 0

Author

Wolfdieter Lang, Jul 15 2013

Keywords

• nonn
• easy
• frac

Comments

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

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).

Links

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 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.

Crossrefs

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

Formula

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