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Expansion of e.g.f. sin(sinh(x))/cos(x), odd powers only.
1

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

%S 1,3,17,203,5473,254067,16540721,1419027899,156472224961,

%T 21673957780323,3688273509233489,756324514461534251,

%U 183915828663739402273,52326057512851162076883,17220068908254192825659249,6490500645147038725191540251,2777808923824765305203681470849

%N Expansion of e.g.f. sin(sinh(x))/cos(x), odd powers only.

%H Robert Israel, <a href="/A009494/b009494.txt">Table of n, a(n) for n = 0..241</a>

%p S:=series(sin(sinh(x))/cos(x),x,51):

%p seq(coeff(S,x,j)*j!,j=1..50,2); # _Robert Israel_, Aug 21 2018

%t With[{nn=50},Take[CoefficientList[Series[Sin[Sinh[x]]/Cos[x],{x,0,nn}],x]Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Dec 04 2012 *)

%o (Magma) m:=40; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1+Sin(Sinh(x))/Cos(x))); [Factorial(n-1)*b[n]: n in [2..m by 2]]; // _Vincenzo Librandi_, Aug 22 2018

%K nonn

%O 0,2

%A _R. H. Hardin_

%E Extended and signs tested by _Olivier GĂ©rard_, Mar 15 1997

%E More terms from _Harvey P. Dale_, Dec 04 2012