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

0,3

Links

Table of n, a(n) for n=0..24.

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

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 *)

Prog

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

Crossrefs

Cf. A000387.

Sequence in context: A012888 A012893 A013075 * A141516 A235378 A214327

Adjacent sequences: A009278 A009279 A009280 * A009282 A009283 A009284

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

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

Status

approved