A009437 Expansion of e.g.f. log(1+x)/exp(sinh(x)).

0, 1, -3, 8, -28, 119, -581, 3345, -22352, 170889, -1480881, 14361885, -154177068, 1814792589, -23230500541, 321160966833, -4767464107904, 75612375796689, -1275789176648193, 22815192314465685, -431023517858496044

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..448

Crossrefs

Cf. A009405 - A009420, A009422 - A009436, A009438, A009439.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!(Laplace( Log(1+x)*Exp(-Sinh(x)) ))); // G. C. Greubel, Sep 08 2023

Mathematica

With[{nn=20},CoefficientList[Series[Log[1+x]/Exp[Sinh[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Oct 01 2013 *)

SageMath

def A009437_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)*exp(-sinh(x)) ).egf_to_ogf().list()
A009437_list(31) # G. C. Greubel, Sep 08 2023

Formula

a(n) ~ (n-1)! * (-1)^(n+1) * exp(sinh(1)). - Vaclav Kotesovec, Jan 23 2015

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Definition clarified by Harvey P. Dale, Oct 01 2013