|
%I #24 Jul 21 2018 20:54:52
%S 1,1,-3,-3,665,-25031,607893,13065717,-3684215119,322746228337,
%T -2173907680851,-5317484317809939,1007358319257596489,
%U 46704901267812186793,-111828938184578058229947,54497429277597236190513381,-19349766542166780916394521759
%N Expansion of e.g.f.: 1/cos(tanh(x)) (even-indexed coefficients only).
%H G. C. Greubel, <a href="/A009011/b009011.txt">Table of n, a(n) for n = 0..200</a> (terms 0..50 from Vincenzo Librandi)
%e 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 +...
%t f[x_] := Sec@Tanh[x]; Table[Derivative[2*n][f][0], {n, 0, 16}] (* _Arkadiusz Wesolowski_, Aug 18 2012 *)
%t 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 *)
%o (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
%K sign
%O 0,3
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
%E a(15), a(16) from _Arkadiusz Wesolowski_, Aug 18 2012
|
