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%I #18 Sep 08 2022 08:44:38
%S 1,0,-12,-360,-14000,-705600,-42520896,-2581394816,-50539790080,
%T 43910434596864,18893865109070848,6357906196273494016,
%U 1895076999147133456384,366371561754009899909120,-176926962056569654501195776,-397908136700956338408562851840,-528899949644745117870350321778688
%N Expansion of e.g.f. cos(tan(x)*arcsin(x)) (even powers only).
%H Robert Israel, <a href="/A012379/b012379.txt">Table of n, a(n) for n = 0..225</a>
%e 1 - (12/4!)*x^4 - (360/6!)*x^6 - (14000/8!)*x^8 - ...
%p S:= series(cos(tan(x)*arcsin(x)),x,51):
%p seq(coeff(S,x,2*j)*(2*j)!,j=0..25); # _Robert Israel_, Jan 06 2019
%t With[{nn=30},Take[CoefficientList[Series[Cos[Tan[x]ArcSin[x]],{x,0,nn}], x]Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Jan 26 2012 *)
%o (Magma) m:=40; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!Cos(Tan(x)*Arcsin(x))); [Factorial(n-1)*b[n]: n in [1..m-1 by 2]]; // _Vincenzo Librandi_, Jan 07 2019
%K sign
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E More terms from _Robert Israel_, Jan 06 2019
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