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

Author

Wolfdieter Lang, Jul 16 2013

Keywords

• nonn
• easy
• frac

Comments

See the comments, references and links under A227570.

Examples

			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.
		

Crossrefs

Cf. A227570, A027641/A027642.

Programs

Mathematica

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

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).