A009436 Expansion of e.g.f. log(1+x)/exp(sin(x)).

0, 1, -3, 8, -20, 59, -261, 1665, -12368, 99945, -888961, 8802045, -96423788, 1154791637, -14982150197, 209295667833, -3133083877248, 50039962416625, -849332973526881, 15266142375582901, -289679348425382572

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..450

Crossrefs

Cf. A009405 - A009420, A009422 - A009435, A009437 - A009439.

Programs

Magma

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

Mathematica

With[{m=30}, CoefficientList[Series[Log[1+x]/E^Sin[x], {x,0,m}], x]*Range[0,m]!] (* Vaclav Kotesovec, Jan 23 2015 *)

SageMath

def A009436_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)*exp(-sin(x)) ).egf_to_ogf().list()
A009436_list(31) # G. C. Greubel, Sep 08 2023

Formula

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

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997