A009438 Expansion of e.g.f. log(1+x)/exp(tan(x)).

0, 1, -3, 8, -32, 149, -831, 5340, -38744, 316161, -2846611, 28263960, -305651048, 3593550245, -45584631743, 622159233948, -9091059243792, 141783419182561, -2351573180823939, 41355560621409352, -768924714448510480

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

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

Programs

Magma

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

Mathematica

With[{nn=20},CoefficientList[Series[Log[1+x]/Exp[Tan[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jan 28 2014 *)

SageMath

def A009438_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)*exp(-tan(x)) ).egf_to_ogf().list()
A009438_list(31) # G. C. Greubel, Sep 08 2023

Formula

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

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Prior Mathematica program corrected by Harvey P. Dale, Jan 28 2014