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

0,2

Comments

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

Links

Table of n, a(n) for n=0..57.

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).

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A063921 A346044 A334402 * A214869 A021632 A248191

Adjacent sequences: A227571 A227572 A227573 * A227575 A227576 A227577

Keyword

nonn,easy,frac

Author

Wolfdieter Lang, Jul 17 2013

Status

approved