A009009 - OEIS

%I #35 Jul 21 2018 20:26:56

%S 1,1,9,177,6545,387649,33646041,4025701617,635120351777,

%T 127753094128897,31911422805749673,9691219439564235441,

%U 3516474983468155702193,1502487398886128051614273,746659439867912626958616441,427003792367575880943003380721

%N Expansion of e.g.f.: 1/cos(sinh(x)) (even-indexed coefficients only).

%H G. C. Greubel, <a href="/A009009/b009009.txt">Table of n, a(n) for n = 0..200</a> (terms 0..50 from Vincenzo Librandi)

%F a(n) ~ (2*n)! * 4 / (sqrt(4+Pi^2) * (log((Pi+sqrt(4+Pi^2))/2))^(2*n+1)). - _Vaclav Kotesovec_, Jan 22 2015

%t f[x_] := Sec@Sinh[x]; Table[Derivative[2*n][f][0], {n, 0, 15}] (* _Arkadiusz Wesolowski_, Aug 18 2012 *)

%t With[{nn=30}, Take[CoefficientList[Series[1/Cos[Sinh[x]], {x,0,nn}], x] Range[0,nn]!, {1,-1,2}]] (* _Harvey P. Dale_, Oct 09 2012 *)

%o (PARI) x='x+O('x^50); v=Vec(serlaplace(1/cos(sinh(x)))); vector(#v\2,n,v[2*n-1]) \\ _G. C. Greubel_, Jul 21 2018

%K nonn

%O 0,3

%A _R. H. Hardin_

%E Extended and signs tested by _Olivier Gérard_, Mar 15 1997

%E a(14), a(15) from _Arkadiusz Wesolowski_, Aug 18 2012