A009435 Expansion of e.g.f.: log(1+x)/cosh(x).

0, 1, -1, -1, 0, 29, -105, 139, -2072, 31737, -247545, 1824151, -22456104, 313750293, -3929185169, 51584719523, -793292190480, 13137192234225, -221862616530705, 3947317975733039, -75492532592047280, 1522475446731094285

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..449

Crossrefs

Cf. A009405 - A009420, A009422 - A009434, A009436 - A009439.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!(Laplace( Log(1+x)/Cosh(x) ))); // G. C. Greubel, Sep 06 2023

Mathematica

With[{nn=30},CoefficientList[Series[Log[1+x]/Cosh[x],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Oct 01 2014 *)

PARI

my(x='x+O('x^30)); concat([0],Vec(serlaplace(log(1+x)/cosh(x)))) \\ Joerg Arndt, Sep 06 2023

SageMath

def A009435_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)/cosh(x) ).egf_to_ogf().list()
A009435_list(40) # G. C. Greubel, Sep 06 2023

Formula

a(n) ~ (-1)^(n+1) * (n-1)! / cosh(1). - Vaclav Kotesovec, Oct 01 2014

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Definition clarified and prior Mathematica program replaced by Harvey P. Dale, Oct 01 2014