A120087 Denominators of expansion of Debye function for n=4: D(4,x).

1, 5, 18, 1, 1440, 1, 75600, 1, 3628800, 1, 167650560, 1, 5230697472000, 1, 336259123200, 1, 53353114214400000, 1, 28100018194440192000, 1, 4817145976189747200000, 1, 91657150256046735360000, 1

Offset

0,2

Comments

From Wolfdieter Lang, Jul 17 2013: (Start)

The numerators are given in A120086.

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)

Links

G. C. Greubel, Table of n, a(n) for n = 0..440

Formula

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).

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

Example

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

Mathematica

Table[Denominator[4*BernoulliB[n]/((n+4)*n!)], {n, 0, 50}] (* G. C. Greubel, May 02 2023 *)

Prog

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

Crossrefs

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

Sequence in context: A116911 A351890 A097491 * A353690 A180135 A260080

Adjacent sequences: A120084 A120085 A120086 * A120088 A120089 A120090

Keyword

nonn,easy,frac

Author

Wolfdieter Lang, Jul 20 2006

Status

approved