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Denominators of rationals with e.g.f. D(4,x), a Debye function.
4

%I #12 Dec 08 2023 23:36:47

%S 1,5,9,1,60,1,105,1,90,1,231,1,10920,1,27,1,2550,1,4389,1,1980,1,897,

%T 1,19110,1,45,1,6960,1,121737,1,4590,1,57,1,19191900,1,63,1,148830,1,

%U 20769,1,8280,1,3525,1,603330,1,891,1,22260,1,11571,1,13050,1

%N Denominators of rationals with e.g.f. D(4,x), a Debye function.

%C See the comments and the Abramowitz-Stegun link under A227573.

%F a(n) = denominator(4*B(n)/(n+4)), n >= 0, with the Bernoulli numbers B(n) = A027641(n)/A027642(n).

%F The e.g.f. of the rationals r(4,n) := 4*B(n)/(n+4) is D(4,x) = (4/x^4)*int(t^4/(exp(t) - 1), t=0..x).

%e The rationals r(4,n), n=0..15 are: 1, -2/5, 1/9, 0, -1/60, 0, 1/105, 0, -1/90, 0, 5/231, 0, -691/10920, 0, 7/27, 0.

%t A227574[n_]:=Denominator[4BernoulliB[n]/(n+4)];

%t Array[A227574,100,0] (* _Paolo Xausa_, Dec 08 2023 *)

%Y Cf. A227573, A027641/A027642, A120086/A120087 (D(4,x) as o.g.f.).

%K nonn,easy,frac

%O 0,2

%A _Wolfdieter Lang_, Jul 17 2013