A003702 Expansion of tan(x)/cosh(x).

1, -1, 21, -141, 10441, -183481, 29429661, -987318021, 276117553681, -15085947275761, 6514632269358501, -526614587249608701, 324871912636292700121, -36433570919762397948841, 30417659816002454665514541

Offset: 0

Author

R. H. Hardin, Simon Plouffe

Keywords

• sign

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..240 (first 50 terms from T. D. Noe)

Programs

Mathematica

Tan[ x ]/Cosh[ x ] (* Odd Part *)
nn = 20; Table[(CoefficientList[Series[Sech[x]*Tan[x], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 16 2015 *)

Formula

a(n) ~ (2*exp(Pi/2) + (exp(Pi) - 1)*(-1)^n) * (2*n+1)! * 2^(2*n+3) / ((1+exp(Pi)) * Pi^(2*n+2)). - Vaclav Kotesovec, Feb 16 2015