A009832 Expansion of e.g.f. tanh(x)*exp(x).

0, 1, 2, 1, -4, 1, 62, 1, -1384, 1, 50522, 1, -2702764, 1, 199360982, 1, -19391512144, 1, 2404879675442, 1, -370371188237524, 1, 69348874393137902, 1, -15514534163557086904, 1, 4087072509293123892362, 1, -1252259641403629865468284, 1

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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

Sequence in context: A145998 A218952 A177413 * A016445 A244554 A364953

Adjacent sequences: A009829 A009830 A009831 * A009833 A009834 A009835

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Definition clarified by Harvey P. Dale, Aug 18 2012

Status

approved