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Expansion of e.g.f. tanh(arcsinh(x)*arctan(x)) (only even powers).
0

%I #20 Jan 25 2025 04:28:45

%S 0,2,-12,-2,10248,-914598,58990140,390971670,-1399074591600,

%T 414051949573170,-75189740418805500,-1988456671385842770,

%U 10786170755283590925720,-6649588570098570005749110,2348244702630162770320062540,166785234190504460598054627270,-1188356567924627353096569058456800

%N Expansion of e.g.f. tanh(arcsinh(x)*arctan(x)) (only even powers).

%e E.g.f. = 2/2!*x^2 - 12/4!*x^4 - 2/6!*x^6 + 10248/8!*x^8...

%t nmax=13; Join[{0}, DeleteElements[CoefficientList[Series[Tanh[ArcSinh[x]ArcTan[x]],{x,0,2*nmax}], x], {0}] (2Range[nmax])!] (* _Stefano Spezia_, Jan 24 2025 *)

%Y Cf. A012160, A012626.

%K sign,changed

%O 0,2

%A Patrick Demichel (patrick.demichel(AT)hp.com)

%E Missing a(0) = 0 added by _Stefano Spezia_, Jan 24 2025

%E a(14)-a(16) from _Stefano Spezia_, Jan 25 2025