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%I #15 May 01 2023 18:02:39
%S 1,8,20,1,1680,1,90720,1,4435200,1,207567360,1,6538371840000,1,
%T 423437414400,1,67580611338240000,1,35763659520196608000,1,
%U 6155242080686899200000,1,117509166994931712000000,1
%N Denominators of expansion for original Debye function (n=3).
%C Numerators are given in A120080.
%C See A120070 for the definition of the Debye function D(x)=D(3,x) and references and links.
%H G. C. Greubel, <a href="/A120081/b120081.txt">Table of n, a(n) for n = 0..500</a>
%F a(n) = denominator(r(n)), with r(n) = [x^n]( 1 - 3*x/8 + Sum_{k >= 0}((B(2*k)/((2*k+3)*(2*k)!))*x^(2*k) ), where B(2*k) = A000367(k)/A002445(k) (Bernoulli numbers).
%F a(n) = denominator( 3*Bernoulli(n)/((n+3)*n!) ), n >= 0. - _G. C. Greubel_, May 01 2023
%t max = 26; Denominator[CoefficientList[Integrate[Normal[Series[(3*(t^3/(Exp[t] -1)))/x^3, {t, 0, max}]], {t, 0, x}], x]] (* _Jean-François Alcover_, Oct 04 2011 *)
%t Table[Denominator[3*BernoulliB[n]/((n+3)*n!)], {n,0,50}] (* _G. C. Greubel_, May 01 2023 *)
%o (Magma) [Denominator(3*Bernoulli(n)/((n+3)*Factorial(n))): n in [0..50]]; // _G. C. Greubel_, May 01 2023
%o (SageMath)
%o def A120081(n): return denominator(3*bernoulli(n)/((n+3)*factorial(n)))
%o [A120081(n) for n in range(51)] # _G. C. Greubel_, May 01 2023
%Y Cf. A000367, A002445, A120080.
%K nonn,easy,frac
%O 0,2
%A _Wolfdieter Lang_, Jul 20 2006
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