A009126 Expansion of e.g.f. cosh(log(1+tanh(x))).

1, 0, 1, -3, 4, 0, 16, -168, 64, 3840, 256, -177408, 1024, 11182080, 4096, -951886848, 16384, 104932638720, 65536, -14544442687488, 262144, 2475749026037760, 1048576, -507711943255523328, 4194304, 123460740095095603200, 16777216

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..250

Formula

E.g.f.: (1/Q(0)+Q(0))/2, where Q(k) = 1 - x/( 2*k+1 + x/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Dec 20 2013

Mathematica

With[{nn=30}, CoefficientList[Series[Cosh[Log[1+Tanh[x]]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 18 2014 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+tanh(x))))) \\ G. C. Greubel, Jul 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+Tanh(x))))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 28 2018

Crossrefs

Cf. A009570.

Sequence in context: A099447 A078067 A192442 * A322278 A102222 A171657

Adjacent sequences: A009123 A009124 A009125 * A009127 A009128 A009129

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Previous Mathematica program replaced and definition clarified by Harvey P. Dale, May 18 2014

Status

approved