A009108 Expansion of e.g.f. cos(x)/cosh(log(1+x)).

1, 0, -2, 3, 1, -30, 164, -525, -391, 22428, -206686, 1039995, 1161337, -96216978, 1241356024, -8517557685, -12681799919, 1373978443800, -22791296600794, 198084321525267, 368659923645521, -49339565916861990

Offset

0,3

Links

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

Formula

a(n) ~ n! * (exp(-1) * sin(1 + (3*n+1)*Pi/4) - exp(1) * sin(1 - (3*n+1)*Pi/4)) / 2^((n+1)/2). - Vaclav Kotesovec, Jul 28 2018

a(n)+a(n+2*p) is divisible by p for any prime p. - Mark van Hoeij, Jun 13 2019

Mathematica

With[{nmax = 30}, CoefficientList[Series[Cos[x]/Cosh[Log[1 + x]], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jul 26 2018 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(cos(x)/cosh(log(1+x)))) \\ G. C. Greubel, Jul 26 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(x)/Cosh(Log(1+x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 26 2018

Crossrefs

Sequence in context: A145142 A137738 A350624 * A016537 A346381 A106385

Adjacent sequences: A009105 A009106 A009107 * A009109 A009110 A009111

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved