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A120084 Numerators of expansion for Debye function for n=2: D(2,x). 2
1, -1, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -691, 0, 1, 0, -3617, 0, 43867, 0, -174611, 0, 77683, 0, -236364091, 0, 657931, 0, -3392780147, 0, 1723168255201, 0, -7709321041217, 0, 151628697551, 0, -26315271553053477373 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,13

COMMENTS

Denominators are found under A120085.

This sequence appears to coincide with A120082.

LINKS

Table of n, a(n) for n=0..36.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

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 a factor (x^2)/2 extracted.

W. Lang: Rationals r(n).

FORMULA

a(n)=numerator(r(n)), with r(n):=[x^n](1 - 2*x/(2*(2+1)) + sum((B(2*k)/((k+1)*(2*k)!))*x^(2*k), 0,..infinity)), |x|<2*Pi. B(2*k):=A000367(k)/A002445(k) (Bernoulli numbers).

EXAMPLE

Rationals r(n): [1, -1/3, 1/24, 0, -1/2160, 0, 1/120960, 0,

-1/6048000, 0, 1/287400960,...].

MATHEMATICA

max = 38; Numerator[ CoefficientList[ Integrate[ Normal[ Series[ (2*(t^2/(Exp[t]-1)))/x^2, {t, 0, max}]], {t, 0, x}], x]] (* Jean-Fran├žois Alcover, Oct 04 2011 *)

CROSSREFS

Sequence in context: A263114 A214335 A060054 * A120082 A249699 A141588

Adjacent sequences:  A120081 A120082 A120083 * A120085 A120086 A120087

KEYWORD

sign,frac

AUTHOR

Wolfdieter Lang, Jul 20 2006

STATUS

approved

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Last modified August 19 23:59 EDT 2022. Contains 356231 sequences. (Running on oeis4.)