A009008 Expansion of e.g.f.: 1/cos(sin(x)) (even-indexed coefficients only).

1, 1, 1, -23, -415, 849, 421089, 16027897, -602344127, -137830187103, -6375572516543, 1282077224074761, 294398207479497377, 6767832711454751473, -10535904130516747834591, -2468712006908963695579879, 172926818125145929773139073

Offset: 0

Author

R. H. Hardin, Simon Plouffe

Keywords

• sign

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100 (first 51 terms from Vincenzo Librandi)

Programs

Mathematica

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

Extensions

a(16) from Arkadiusz Wesolowski, Aug 18 2012