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%I #12 Apr 29 2014 22:40:33
%S 1,0,8,-392,20096,-1754368,241340032,-44833033216,10840711614464,
%T -3348758074142720,1285112610745352192,-598690046386495291392,
%U 332953969072425739124736,-217949438999618554495500288
%N Expansion of e.g.f. of arctan(sec(x)*arcsinh(x)) (odd coefficients only).
%C arctan(sec(x)*arcsinh(x)) = x + 8/5!*x^5 - 392/7!*x^7 + 20096/9!*x^9 ...
%e a(0) = 1! * (coefficient of x^1 term) = 1.
%e a(1) = 3! * (coefficient of x^3 term) = 0.
%e a(2) = 5! * (coefficient of x^5 term) = 8.
%t With[{nn=30},Take[CoefficientList[Series[ArcTan[Sec[x]ArcSinh[x]],{x,0,nn}],x] Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Jul 31 2013 *)
%K sign
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)