A009281 Expansion of e.g.f. exp(x)*cosh(log(1+x)).

1, 1, 2, 1, 7, -19, 136, -923, 7421, -66743, 667486, -7342279, 88107427, -1145396459, 16035550532, -240533257859, 3848532125881, -65425046139823, 1177650830516986, -22375365779822543, 447507315596451071, -9397653627525472259, 206748379805560389952, -4755212735527888968619, 114125105652669335247157

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Crossrefs

Cf. A000387.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[x]*Cosh[Log[1+x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Sep 02 2016 *)
CoefficientList[Series[(E^x*(1 + (1 + x)^2))/(2*(1 + x)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 22 2015 *)

PARI

my(x='x+O('x^66)); Vec(serlaplace(exp(x)*cosh(log(1+x)))) \\ Joerg Arndt, Jan 05 2024

Formula

a(n) ~ n! * (-1)^n / (2*exp(1)). - Vaclav Kotesovec, Jan 22 2015

a(n) = ((-1)^n * A000387(n)) + 1. - Christian Krause, Jan 05 2024

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Prior Mathematica program replaced by Harvey P. Dale, Sep 02 2016