A009281 - OEIS

%I #24 Jan 05 2024 07:56:36

%S 1,1,2,1,7,-19,136,-923,7421,-66743,667486,-7342279,88107427,

%T -1145396459,16035550532,-240533257859,3848532125881,-65425046139823,

%U 1177650830516986,-22375365779822543,447507315596451071,-9397653627525472259,206748379805560389952,-4755212735527888968619,114125105652669335247157

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

%F a(n) ~ n! * (-1)^n / (2*exp(1)). - _Vaclav Kotesovec_, Jan 22 2015

%F a(n) = ((-1)^n * A000387(n)) + 1. - _Christian Krause_, Jan 05 2024

%t With[{nn=20},CoefficientList[Series[Exp[x]*Cosh[Log[1+x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Sep 02 2016 *)

%t CoefficientList[Series[(E^x*(1 + (1 + x)^2))/(2*(1 + x)), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 22 2015 *)

%o (PARI) my(x='x+O('x^66)); Vec(serlaplace(exp(x)*cosh(log(1+x)))) \\ _Joerg Arndt_, Jan 05 2024

%Y Cf. A000387.

%K sign,easy

%O 0,3

%A _R. H. Hardin_

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

%E Prior Mathematica program replaced by _Harvey P. Dale_, Sep 02 2016