A227571 Denominators of rationals with e.g.f. D(3,x), a Debye function.

1, 8, 10, 1, 70, 1, 126, 1, 110, 1, 286, 1, 13650, 1, 34, 1, 3230, 1, 5586, 1, 2530, 1, 1150, 1, 24570, 1, 58, 1, 8990, 1, 157542, 1, 5950, 1, 74, 1, 24949470, 1, 82, 1, 193930, 1, 27090, 1, 10810, 1, 4606, 1, 788970, 1, 1166, 1, 29150, 1, 15162, 1

Offset

0,2

Comments

See the comments, references and links under A227570.

Links

Table of n, a(n) for n=0..55.

Formula

a(n) = denominator(3*B(n)/(n+3)), n >= 0, with the Bernoulli numbers B(n) = A027641(n)/A027642(n).

The e.g.f. of the rationals r(3,n) := 3*B(n)/(n+3) is D(3,x) = (3/x^3)*int(t^3/(exp(x) - 1), t=0..x).

Example

The rationals r(3,n), n=0..15 are: 1, -3/8, 1/10, 0, -1/70, 0, 1/126, 0, -1/110, 0, 5/286, 0, -691/13650, 0, 7/34, 0.

Mathematica

A227571[n_]:=Denominator[3BernoulliB[n]/(n+3)];
Array[A227571, 100, 0] (* Paolo Xausa, Dec 08 2023 *)

Crossrefs

Cf. A227570, A027641/A027642.

Sequence in context: A114132 A038704 A229196 * A112590 A105386 A124685

Adjacent sequences: A227568 A227569 A227570 * A227572 A227573 A227574

Keyword

nonn,easy,frac

Author

Wolfdieter Lang, Jul 16 2013

Status

approved