A176327 Numerators of the rational sequence with e.g.f. (x/2)*(1+exp(-x))/(1-exp(-x)).

1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 5, 0, -691, 0, 7, 0, -3617, 0, 43867, 0, -174611, 0, 854513, 0, -236364091, 0, 8553103, 0, -23749461029, 0, 8615841276005, 0, -7709321041217, 0, 2577687858367, 0, -26315271553053477373, 0, 2929993913841559, 0, -261082718496449122051

Offset: 0

Author

Paul Curtz, Apr 15 2010

Keywords

• sign

Comments

Numerator of the Bernoulli number B_n, except B(1)=0.

A027641 is the main entry for this sequence, which is only a minor variation. - N. J. A. Sloane, Nov 29 2010.

This could formally be defined by building the arithmetic mean of the numerators in A164555(n) and A027641(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A176289 (denominators), A027642, A141056, A164020, A165823

Programs

Maple

seq(numer((bernoulli(i,0)+bernoulli(i,1))/2),i=0..40); # Peter Luschny, Jun 17 2012

Mathematica

terms = 41; egf = (x/2)*((1 + Exp[-x])/(1 - Exp[-x])) + O[x]^(terms+1);
CoefficientList[egf, x]*Range[0, terms-1]! // Numerator (* Jean-François Alcover, Jun 13 2017 *)

PARI

apply(numerator, Vec(serlaplace((x/2)*(1+exp(-x))/(1-exp(-x))))) \\ Charles R Greathouse IV, Sep 26 2017

Formula

a(2n+1) = 0. a(2n ) = A000367(n).

a(n) = A164555(n) = A027641(n) if n <>1.

Extensions

New name from Peter Luschny, Jun 18 2012