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A009196
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Expansion of e.g.f. exp(log(1+x)/cos(x)).
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1
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1, 1, 0, 3, 6, 15, 195, 126, 6860, 10581, 275955, 1581734, 11684442, 223836379, 423165561, 32439219242, 10301267912, 4976257880345, 4959730228167, 803695677341350, 3521551886934550, 131556027669677615, 1743242423131143869, 19663074849601180770
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OFFSET
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0,4
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COMMENTS
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Note that a(27) is negative. - Vaclav Kotesovec, Jan 24 2015
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 0..200
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FORMULA
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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
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MATHEMATICA
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Exp[ Log[ 1+x ]/Cos[ x ] ]
CoefficientList[Series[(1 + x)^Sec[x], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 24 2015 *)
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PROG
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(PARI) seq(n)={my(x='x+O('x^n)); Vec(serlaplace(exp(log(1+x)/cos(x))))} \\ Andrew Howroyd, Feb 25 2018
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CROSSREFS
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Sequence in context: A013271 A013272 A013278 * A329124 A116613 A291803
Adjacent sequences: A009193 A009194 A009195 * A009197 A009198 A009199
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KEYWORD
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sign,easy
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AUTHOR
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R. H. Hardin
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EXTENSIONS
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Extended with signs by Olivier Gérard, Mar 15 1997
a(22)-a(23) from Andrew Howroyd, Feb 25 2018
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STATUS
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approved
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