A009137 Expansion of e.g.f. cosh(log(1+x)/cos(x)).

1, 0, 1, -3, 24, -120, 990, -7140, 69048, -658728, 7542960, -89216160, 1191378408, -16691737920, 255303337016, -4111553595240, 70932973452032, -1287129875516672, 24738396315075648, -498729120183554688

Offset

0,4

Links

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

Formula

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

Maple

seq(coeff(series(factorial(n)*cosh(log(1+x)/cos(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]/Cos[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)/cos(x)))) \\ G. C. Greubel, Jul 30 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+x)/Cos(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 30 2018

Crossrefs

Sequence in context: A324065 A151883 A009134 * A319097 A326789 A305543

Adjacent sequences: A009134 A009135 A009136 * A009138 A009139 A009140

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved