A009322 Expansion of e.g.f. log(1+log(1+x)/cos(x)).

0, 1, -2, 10, -53, 393, -3469, 36923, -455034, 6408445, -101394621, 1782112451, -34444229280, 726178939315, -16584374311751, 407872396640525, -10747392535828704, 302068718096449161, -9020579203256189193, 285223376077563766015, -9519540878894689112808

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) ~ (n-1)! * (-1)^(n+1) / r^n, where r = 0.56927728739385569796597499937305463781561716... is the root of the equation exp(cos(r))*(1-r) = 1. - Vaclav Kotesovec, Jan 24 2015

Maple

egf:= log(1+log(1+x)/cos(x)):
a:= n-> n! * coeff(series(egf, x, n+1), x, n):
seq(a(n), n=0..20); # Alois P. Heinz, Dec 12 2012

Mathematica

With[{nn=20}, CoefficientList[Series[Log[1+Log[1+x]/Cos[x]], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Dec 12 2012 *)

Prog

(PARI) Vec(serlaplace(log(1+log(1+x)/cos(x)))) \\ Charles R Greathouse IV, Sep 26 2017

Crossrefs

Sequence in context: A370390 A009320 A204186 * A192697 A102536 A221604

Adjacent sequences: A009319 A009320 A009321 * A009323 A009324 A009325

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved