A009138 - OEIS

%I #26 Sep 08 2022 08:44:37

%S 1,0,1,-3,0,0,210,-1260,3752,-46872,690960,-6013920,58389672,

%T -895065600,12888358392,-168411308520,2621915506688,-47022586623488,

%U 824126273574336,-14767693271763840,293589445235224960

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

%H G. C. Greubel, <a href="/A009138/b009138.txt">Table of n, a(n) for n = 0..250</a>

%F a(n) ~ (-1)^n * n! / (2 * Gamma(1/cosh(1)) * n^(1 - 1/cosh(1))). - _Vaclav Kotesovec_, Jul 31 2018

%p seq(coeff(series(factorial(n)*cosh(log(1+x)/cosh(x)), x,n+1),x,n),n=0..20); # _Muniru A Asiru_, Jul 31 2018

%t With[{nn=30},CoefficientList[Series[Cosh[Log[1+x]/Cosh[x]],{x,0,nn}], x]Range[0,nn]!] (* _Harvey P. Dale_, Jun 05 2012 *)

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

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

%K sign,easy

%O 0,4

%A _R. H. Hardin_

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

%E Definition clarified by _Harvey P. Dale_, Jun 05 2012