%I #15 Jun 21 2024 14:35:07

%S 1,1,1,25,3617,340145,40490657,7034559753,1668333374913,

%T 504856533178465,189500285350524865,86696156445549770233,

%U 47524548345395009982689,30739504895562596416971025,23162222253680333719652996449,20112913566033287819336502367465,19939158697176271310635403636418945

%N Expansion of e.g.f. sec(arctanh(x)*cos(x)), only even powers.

%H Stefano Spezia, <a href="/A012748/b012748.txt">Table of n, a(n) for n = 0..150</a>

%e E.g.f. = 1 + x^2/2! + x^4/4! + 25*x^6/6! + 3617*x^8/8! + ...

%t nmax=32; DeleteCases[CoefficientList[Series[Sec[ArcTanh[x]Cos[x]],{x,0,nmax}],x],0](2Range[0,nmax/2])! (* _Stefano Spezia_, Jun 21 2024 *)

%K nonn

%O 0,4

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

%E a(14)-a(16) from _Stefano Spezia_, Jun 21 2024