OFFSET
0,3
FORMULA
E.g.f. tanh(x)*exp(x).
G.f.: x/U(0)/(1-x) where U(k) = 1 - x + x^2*(k+1)*(k+2)/U(k+1); (continued fraction, 1-step). - Sergei N. Gladkovskii, Oct 14 2012
G.f.: x/(1-x)/Q(0), where Q(k) = 1 + x - x*(k+2)/(1+x*(k+1)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Apr 21 2013
If n is even, a(n) ~ (-1)^(1+n/2) * n! * 2^(n+2)/Pi^(n+1). - Vaclav Kotesovec, Oct 23 2013
MAPLE
G(x):=exp(x)*tanh(x): f[0]:=G(x): for n from 1 to 54 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..27 ); # Zerinvary Lajos, Apr 05 2009
MATHEMATICA
With[{nn=30}, CoefficientList[Series[Tanh[x]Exp[x], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Aug 18 2012 *)
PROG
(PARI) x='x+O('x^66); concat([0], Vec(serlaplace( tanh(x)*exp(x) ) ) ) \\ Joerg Arndt, Apr 21 2013
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
Definition clarified by Harvey P. Dale, Aug 18 2012
STATUS
approved