A120087 - OEIS

%I #11 May 02 2023 05:10:01

%S 1,5,18,1,1440,1,75600,1,3628800,1,167650560,1,5230697472000,1,

%T 336259123200,1,53353114214400000,1,28100018194440192000,1,

%U 4817145976189747200000,1,91657150256046735360000,1

%N Denominators of expansion of Debye function for n=4: D(4,x).

%C From _Wolfdieter Lang_, Jul 17 2013: (Start)

%C The numerators are given in A120086.

%C See the link under A120080 for D(n,4) as e.g.f. of 4*B(n)/(n+4) = A227573(n)/A227574(n), n>= 0. (End)

%H G. C. Greubel, <a href="/A120087/b120087.txt">Table of n, a(n) for n = 0..440</a>

%F a(n) = denominator(r(n)), with r(n) = [x^n](1 - 2*x/5 + 2*Sum_{k >= 0}(B(2*k)/((k+2)*(2*k)!))*x^(2*k) ), |x| < 2*Pi. B(2*k) = A000367(k)/A002445(k) (Bernoulli numbers).

%F a(n) = denominator(4*B(n)/((n+4)*n!), n >= 0, with the Bernoulli numbers B(n) = A027641(n)/A027642(n). From D(4,x) read as o.g.f. _ _Wolfdieter Lang_, Jul 17 2013

%e Rationals r(n): [1, -2/5, 1/18, 0, -1/1440, 0, 1/75600, 0, -1/3628800, 0, 1/167650560, 0, -691/5230697472000, ...].

%t Table[Denominator[4*BernoulliB[n]/((n+4)*n!)], {n,0,50}] (* _G. C. Greubel_, May 02 2023 *)

%o (Magma) [Denominator(4*(n+1)*(n+2)*(n+3)*Bernoulli(n)/Factorial(n+4)): n in [0..50]]; // _G. C. Greubel_, May 02 2023

%o (SageMath) [denominator(4*(n+1)*(n+2)*(n+3)*bernoulli(n)/factorial(n+4)) for n in range(51)] # _G. C. Greubel_, May 02 2023

%Y Cf. A000367, A002445, A027641, A027642, A120080, A120081, A120082, A120083, A120084, A120085, A120086, A227573, A227574.

%K nonn,easy,frac

%O 0,2

%A _Wolfdieter Lang_, Jul 20 2006