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Expansion of e.g.f. log(1+x)/exp(tanh(x)).
9

%I #18 Sep 08 2023 04:04:16

%S 0,1,-3,8,-16,29,-191,1980,-14456,85713,-657171,7877880,-97759608,

%T 1100545341,-13021637695,185198054748,-2933940050000,46990261427073,

%U -774002505048195,13811029423532424,-266175983849182016

%N Expansion of e.g.f. log(1+x)/exp(tanh(x)).

%H G. C. Greubel, <a href="/A009439/b009439.txt">Table of n, a(n) for n = 0..448</a>

%t With[{nn=20},CoefficientList[Series[Log[1+x]/Exp[Tanh[x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, May 19 2023 *)

%o (Magma)

%o R<x>:=PowerSeriesRing(Rationals(), 30);

%o [0] cat Coefficients(R!(Laplace( Log(1+x)*Exp(-Tanh(x)) ))); // _G. C. Greubel_, Sep 08 2023

%o (SageMath)

%o def A009439_list(prec):

%o P.<x> = PowerSeriesRing(QQ, prec)

%o return P( log(1+x)*exp(-tanh(x)) ).egf_to_ogf().list()

%o A009439_list(31) # _G. C. Greubel_, Sep 08 2023

%Y Cf. A009405 - A009420, A009422 - A009438.

%K sign,easy

%O 0,3

%A _R. H. Hardin_

%E Extended with signs by _Olivier GĂ©rard_, Mar 15 1997

%E Definition clarified and previous Mathematica program replaced by _Harvey P. Dale_, May 19 2023