A009139 Expansion of e.g.f. cosh(log(1+x)/exp(x)).

1, 0, 1, -9, 60, -390, 2820, -24010, 238336, -2659104, 32417160, -426027008, 6004088112, -90491148176, 1454386367616, -24843370627920, 449435283828992, -8582294948325760, 172476215457600000, -3638420414864043264

Offset

0,4

Links

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

Formula

a(n) ~ (-1)^n * n! * n^(exp(1) - 1) / (2 * Gamma(exp(1))). - Vaclav Kotesovec, Jul 31 2018

Maple

seq(coeff(series(factorial(n)*cosh(log(1+x)/exp(x)), x, n+1), x, n), n=0..20); # Muniru A Asiru, Jul 31 2018

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A082150 A026785 A153820 * A086018 A197402 A213133

Adjacent sequences: A009136 A009137 A009138 * A009140 A009141 A009142

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved