A009572 - OEIS

%I #23 Jan 22 2018 02:39:22

%S 0,1,-1,0,-6,35,-195,1358,-10892,98037,-980325,10783564,-129402834,

%T 1682236855,-23551315879,353269738170,-5652315810840,96089368784297,

%U -1729608638117193,32862564124226648,-657251282484533150

%N Expansion of e.g.f. sinh(log(1+x))*cos(x).

%H G. C. Greubel, <a href="/A009572/b009572.txt">Table of n, a(n) for n = 0..448</a>

%F a(n) ~ n! * (-1)^(n+1) * cos(1) / 2. - _Vaclav Kotesovec_, Jan 23 2015

%t With[{nn=30},CoefficientList[Series[Sinh[Log[1+x]]Cos[x],{x,0,nn}], x]Range[0,nn]!] (* _Harvey P. Dale_, Mar 09 2012 *)

%t CoefficientList[Series[(x*(2 + x)*Cos[x])/(2*(1 + x)), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 23 2015 *)

%o (PARI) x='x+O('x^30); concat([0], Vec(serlaplace(sinh(log(1+x))*cos(x)))) \\ _G. C. Greubel_, Jan 21 2018

%K sign,easy

%O 0,5

%A _R. H. Hardin_

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