A009009 Expansion of e.g.f.: 1/cos(sinh(x)) (even-indexed coefficients only).

1, 1, 9, 177, 6545, 387649, 33646041, 4025701617, 635120351777, 127753094128897, 31911422805749673, 9691219439564235441, 3516474983468155702193, 1502487398886128051614273, 746659439867912626958616441, 427003792367575880943003380721

Offset: 0

Author

R. H. Hardin

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..200 (terms 0..50 from Vincenzo Librandi)

Programs

Mathematica

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

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

Formula

a(n) ~ (2*n)! * 4 / (sqrt(4+Pi^2) * (log((Pi+sqrt(4+Pi^2))/2))^(2*n+1)). - Vaclav Kotesovec, Jan 22 2015

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997

a(14), a(15) from Arkadiusz Wesolowski, Aug 18 2012