A009817 Expansion of e.g.f. tanh(tan(x)*x) (even powers only).

0, 2, 8, -144, -11264, -323840, 36347904, 8388294656, 620426657792, -168731721990144, -79627879039631360, -11099857853570613248, 5627175549005859913728, 4469405304978356270268416

Offset: 0

Author

R. H. Hardin, Mar 15 1996

Keywords

• sign

Links

• Iain Fox, Table of n, a(n) for n = 0..231 (first 101 terms from Vincenzo Librandi)

Crossrefs

Cf. A000182, A003718, A009707, A024257.

Programs

Maple

S:= series(tanh(tan(x)*x),x,41):
seq(coeff(S,x,n)*n!,n=0..40,2); # Robert Israel, Dec 21 2017

Mathematica

With[{nn=30},Take[CoefficientList[Series[Tanh[Tan[x]*x],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* Harvey P. Dale, Oct 28 2013 *)

PARI

first(n) = x='x+O('x^(2*n-1)); vecextract(Vec(serlaplace(tanh(tan(x)*x)), -2*n), (4^n - 1)/3) \\ Iain Fox, Dec 21 2017

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Prior Mathematica program replaced by Harvey P. Dale, Oct 28 2013