A009196 Expansion of e.g.f. exp(log(1+x)/cos(x)).

1, 1, 0, 3, 6, 15, 195, 126, 6860, 10581, 275955, 1581734, 11684442, 223836379, 423165561, 32439219242, 10301267912, 4976257880345, 4959730228167, 803695677341350, 3521551886934550, 131556027669677615, 1743242423131143869, 19663074849601180770

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Comments

Note that a(27) is negative. - Vaclav Kotesovec, Jan 24 2015

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200

Programs

Mathematica

Exp[ Log[ 1+x ]/Cos[ x ] ]
CoefficientList[Series[(1 + x)^Sec[x], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 24 2015 *)

PARI

seq(n)={my(x='x+O('x^n)); Vec(serlaplace(exp(log(1+x)/cos(x))))} \\ Andrew Howroyd, Feb 25 2018

Formula

a(n) ~ n! * (-1)^n / (GAMMA(-1/cos(1)) * n^(1+1/cos(1))) * (1 - sin(1)*log(n)/((cos(1))^2*n)*(1+1/cos(1))). - Vaclav Kotesovec, Jan 24 2015

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

a(22)-a(23) from Andrew Howroyd, Feb 25 2018