A009011 Expansion of e.g.f.: 1/cos(tanh(x)) (even-indexed coefficients only).

1, 1, -3, -3, 665, -25031, 607893, 13065717, -3684215119, 322746228337, -2173907680851, -5317484317809939, 1007358319257596489, 46704901267812186793, -111828938184578058229947, 54497429277597236190513381, -19349766542166780916394521759

Offset: 0

Author

R. H. Hardin

Keywords

• sign

Examples

			1/cos(tanh x) = 1+ 1*x^2/2! -3*x^4/4! -3*x^6/6! +665*x^8/8! -25031*x^10/10! +... = 1 +x^2/2 -x^4/8 -x^6/240 +19*x^8/1152 -25031*x^10/3628800 +...
		

Links

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

Programs

Mathematica

f[x_] := Sec@Tanh[x]; Table[Derivative[2*n][f][0], {n, 0, 16}] (* Arkadiusz Wesolowski, Aug 18 2012 *)
With[{nmax = 50}, CoefficientList[Series[1/(Cos[Tanh[x]]), {x, 0, nmax}], x]*Range[0, nmax]!][[1 ;; -1 ;; 2]] (* G. C. Greubel, Jul 21 2018 *)

PARI

x='x+O('x^50); v=Vec(serlaplace(1/cos(tanh(x)))); vector(#v\2,n,v[2*n-1]) \\ G. C. Greubel, Jul 21 2018

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

a(15), a(16) from Arkadiusz Wesolowski, Aug 18 2012