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%I #19 Feb 25 2018 20:39:28
%S 1,1,0,3,6,15,195,126,6860,10581,275955,1581734,11684442,223836379,
%T 423165561,32439219242,10301267912,4976257880345,4959730228167,
%U 803695677341350,3521551886934550,131556027669677615,1743242423131143869,19663074849601180770
%N Expansion of e.g.f. exp(log(1+x)/cos(x)).
%C Note that a(27) is negative. - _Vaclav Kotesovec_, Jan 24 2015
%H Andrew Howroyd, <a href="/A009196/b009196.txt">Table of n, a(n) for n = 0..200</a>
%F 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
%t Exp[ Log[ 1+x ]/Cos[ x ] ]
%t CoefficientList[Series[(1 + x)^Sec[x], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 24 2015 *)
%o (PARI) seq(n)={my(x='x+O('x^n)); Vec(serlaplace(exp(log(1+x)/cos(x))))} \\ _Andrew Howroyd_, Feb 25 2018
%K sign,easy
%O 0,4
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
%E a(22)-a(23) from _Andrew Howroyd_, Feb 25 2018