A227574 Denominators of rationals with e.g.f. D(4,x), a Debye function.

1, 5, 9, 1, 60, 1, 105, 1, 90, 1, 231, 1, 10920, 1, 27, 1, 2550, 1, 4389, 1, 1980, 1, 897, 1, 19110, 1, 45, 1, 6960, 1, 121737, 1, 4590, 1, 57, 1, 19191900, 1, 63, 1, 148830, 1, 20769, 1, 8280, 1, 3525, 1, 603330, 1, 891, 1, 22260, 1, 11571, 1, 13050, 1

Offset: 0

Author

Wolfdieter Lang, Jul 17 2013

Keywords

• nonn
• easy
• frac

Comments

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

Examples

			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.
		

Crossrefs

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

Programs

Mathematica

A227574[n_]:=Denominator[4BernoulliB[n]/(n+4)];
Array[A227574,100,0] (* Paolo Xausa, Dec 08 2023 *)

Formula

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

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).