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

0,2

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

Table of n, a(n) for n=0..55.

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.

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.

Crossrefs

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

Sequence in context: A132554 A077275 A059903 * A353701 A246133 A205014

Adjacent sequences: A227537 A227538 A227539 * A227541 A227542 A227543

Keyword

nonn,easy,frac

Author

Wolfdieter Lang, Jul 15 2013

Status

approved