

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

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



KEYWORD

nonn,easy,frac


AUTHOR



STATUS

approved



