

A227540


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


1



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
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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 AbramowitzStegun 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 * A246133 A205014 A204936
Adjacent sequences: A227537 A227538 A227539 * A227541 A227542 A227543


KEYWORD

nonn,easy,frac


AUTHOR

Wolfdieter Lang, Jul 15 2013


STATUS

approved



