A035047 Denominators of alternating sum transform (PSumSIGN) of Harmonic numbers H(n) = A001008/A002805.

1, 2, 3, 4, 15, 12, 105, 24, 315, 120, 3465, 40, 45045, 280, 45045, 560, 765765, 5040, 14549535, 5040, 14549535, 55440, 334639305, 55440, 1673196525, 720720, 5019589575, 720720, 145568097675, 720720

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

Links

• Robert Israel, Table of n, a(n) for n = 1..2000
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A035048.

Programs

Maple

S:= series(log(1-x)/(x^2-1), x, 101):
seq(denom(coeff(S,x,j)),j=1..100); # Robert Israel, Jun 02 2015

PARI

a(n)=denominator(polcoeff(log(1-x)/(x^2-1)+O(x^(n+1)),n))

Formula

G.f. for A035048(n)/A035047(n) : log(1-x)/(x^2-1). - Benoit Cloitre, Jun 15 2003

a(n) = denominator((-1)^(n+1)*1/2*(log(2)+(-1)^(n+1)*(gamma+1/2*(psi(1+n/2)-psi(3/2+n/2))+psi(2+n)))), with gamma the Euler-Mascheroni constant. - [Gerry Martens, Apr 28 2011]