A009437 -id:A009437 - cp's OEIS frontend

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

R. H. Hardin

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

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

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

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

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

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

Extended with signs by Olivier Gérard, Mar 15 1997

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

Original entry on oeis.org

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

Offset: 0

R. H. Hardin

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

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

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

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

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

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

Extended with signs by Olivier Gérard, Mar 15 1997

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

cp's OEIS Frontend

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

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