A009838 Expansion of e.g.f.: tanh(x)/(1+x).

0, 1, -2, 4, -16, 96, -576, 3760, -30080, 278656, -2786560, 30298368, -363580416, 4748913664, -66484791296, 995368112128, -15925889794048, 270949991841792, -4877099853152256, 92635808324780032, -1852716166495600640

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Comments

Unsigned sequence satisfies a(n)=na(n-1)+b(n-1) where b(n) is defined in A009006. E.g.f. tanh(z)/(1-z). - Mario Catalani (mario.catalani(AT)unito.it), Feb 10 2003

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Programs

Maple

G(x):= tanh(x)/(1+x): f[0]:=G(x): for n from 1 to 21 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=0..20); # Zerinvary Lajos, Apr 03 2009

Mathematica

With[{nn=20},CoefficientList[Series[Tanh[x]/(1+x),{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Jul 18 2013 *)

Formula

|a(n)| ~ n! * tanh(1). - Vaclav Kotesovec, Sep 22 2013

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Prior Mathematica program replaced and definition clarified by Harvey P. Dale, Jul 18 2013