A075267 Denominator of the coefficient of x^n in log(-log(1-x)/x).

2, 24, 8, 2880, 288, 362880, 17280, 29030400, 89600, 958003200, 17418240, 31384184832000, 402361344000, 62768369664000, 295206912, 512189896458240000, 342372925440000, 919636959090769920000, 5377993912811520000, 674400436666564608000000, 89903156428800000

Offset: 1

Author

Paul D. Hanna, Sep 15 2002

Keywords

• frac
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..443

Crossrefs

Cf. A075266 (numerator), A075264, A053657.

Programs

Magma

m:=25; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Log(-Log(1-x)/x) )); [Denominator(b[n]): n in [1..m-2]]; // G. C. Greubel, Oct 29 2018

Maple

S:= series(log(-log(1-x)/x),x,51):
seq(denom(coeff(S,x,j)),j=1..50); # Robert Israel, May 17 2016

Mathematica

Denominator[ CoefficientList[ Series[ Log[ -Log[1 - x]/x], {x, 0, 18}], x]]

Formula

a(n) = denominator(Sum_{k=1..n} (k-1)!*(-1)^(n-k-1)*binomial(n,k)*Stirling1(n+k,k)/(n+k)!). - Vladimir Kruchinin, Aug 14 2025

Extensions

Edited by Robert G. Wilson v, Sep 17 2002