A120083 Denominators of expansion for Debye function for n=1: D(1,x).

1, 4, 36, 1, 3600, 1, 211680, 1, 10886400, 1, 526901760, 1, 16999766784000, 1, 1120863744000, 1, 181400588328960000, 1, 97072790126247936000, 1, 16860010916664115200000, 1, 324325300906011525120000, 1

Offset: 0

Author

Wolfdieter Lang, Jul 20 2006

Keywords

• nonn
• easy
• frac

Comments

Numerators are found under A120082.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..447

Crossrefs

Cf. A120082.

Programs

Magma

[Denominator(Bernoulli(n)/Factorial(n+1)): n in [0..50]]; // G. C. Greubel, May 01 2023

Mathematica

Table[Denominator[BernoulliB[n]/(n+1)!], {n,0,50}] (* G. C. Greubel, May 01 2023 *)

SageMath

def A120083(n): return denominator(bernoulli(n)/factorial(n+1))
[A120083(n) for n in range(51)] # G. C. Greubel, May 01 2023

Formula

a(n) = denominator(r(n)), with r(n) = [x^n]( 1 - x/4 + Sum_{k >= 0}(B(2*k)/((2*k+1)*(2*k)!))*x^(2*k) ), |x|<2*pi. B(2*k) = A000367(k)/A002445(k) (Bernoulli numbers).

a(n) = denominator(B(n)/(n+1)!), n >= 0. See the comment on the e.g.f. D(1,x) in A120082. - Wolfdieter Lang, Jul 15 2013