A009552 - OEIS

%I #20 Jan 22 2018 02:55:55

%S 0,1,0,2,-12,71,-540,4780,-48328,549601,-6944040,96496894,-1462695300,

%T 24016678583,-424638675188,8043741624464,-162517240830480,

%U 3488577094105985,-79287238580689872,1902063885622909594

%N Expansion of e.g.f. sin(x)/cos(log(1+x)).

%H G. C. Greubel, <a href="/A009552/b009552.txt">Table of n, a(n) for n = 0..432</a>

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

%t Sin[ x ]/Cos[ Log[ 1+x ] ]

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

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

%K sign,easy

%O 0,4

%A _R. H. Hardin_

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