A009126 - OEIS

%I #21 Sep 08 2022 08:44:37

%S 1,0,1,-3,4,0,16,-168,64,3840,256,-177408,1024,11182080,4096,

%T -951886848,16384,104932638720,65536,-14544442687488,262144,

%U 2475749026037760,1048576,-507711943255523328,4194304,123460740095095603200,16777216

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

%H G. C. Greubel, <a href="/A009126/b009126.txt">Table of n, a(n) for n = 0..250</a>

%F E.g.f.: (1/Q(0)+Q(0))/2, where Q(k) = 1 - x/( 2*k+1 + x/Q(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Dec 20 2013

%t With[{nn=30},CoefficientList[Series[Cosh[Log[1+Tanh[x]]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, May 18 2014 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+tanh(x))))) \\ _G. C. Greubel_, Jul 28 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+Tanh(x))))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 28 2018

%Y Cf. A009570.

%K sign,easy

%O 0,4

%A _R. H. Hardin_

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

%E Previous Mathematica program replaced and definition clarified by _Harvey P. Dale_, May 18 2014