A009437 - OEIS

%I #22 Sep 08 2023 04:04:47

%S 0,1,-3,8,-28,119,-581,3345,-22352,170889,-1480881,14361885,

%T -154177068,1814792589,-23230500541,321160966833,-4767464107904,

%U 75612375796689,-1275789176648193,22815192314465685,-431023517858496044

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

%H G. C. Greubel, <a href="/A009437/b009437.txt">Table of n, a(n) for n = 0..448</a>

%F a(n) ~ (n-1)! * (-1)^(n+1) * exp(sinh(1)). - _Vaclav Kotesovec_, Jan 23 2015

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

%o (Magma)

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

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

%o (SageMath)

%o def A009437_list(prec):

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

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

%o A009437_list(31) # _G. C. Greubel_, Sep 08 2023

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

%K sign,easy

%O 0,3

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997

%E Definition clarified by _Harvey P. Dale_, Oct 01 2013