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%I #9 Apr 23 2024 19:56:48
%S 0,2,12,-98,-16968,-780838,93371652,31402903222,2306688997872,
%T -1741952370835918,-849143623135762308,-14075683397521166258,
%U 228742196475611564627112,136676421833398225367464202,-34106209758743782233592937868,-128144470665734286260829913072538
%N Expansion of e.g.f. arctan(sinh(x)*tan(x)) (even powers only).
%e 0/0!*x^0 + 2/2!*x^2 + 12/4!*x^4 - 98/6!*x^6 - 16968/8!*x^8 ...
%p egf := arctan(tan(x)*sinh(x)): ser := series(egf, x, 33):
%p seq((2*n)!*coeff(ser, x, 2*n), n = 0..15); # _Peter Luschny_, Apr 23 2024
%t With[{nn=30},Take[CoefficientList[Series[ArcTan[Sinh[x]Tan[x]],{x,0,nn}],x] Range[0, nn]!, {1,-1,2}]] (* _Harvey P. Dale_, Oct 17 2015 *)
%Y Cf. A012816.
%K sign
%O 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E Missing a(0) = 0 prepended and new name by _Peter Luschny_, Apr 23 2024