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A191719
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Expansion of e.g.f. arctan(x*exp(x)).
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7
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0, 1, 2, 1, -20, -151, -354, 6217, 100472, 537777, -7631270, -223395919, -2120164188, 22050300505, 1154262915638, 17130776734905, -105423782758544, -11372993234072863, -245877012220234446, 345837436238423521, 188329590656514108380
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = n!*Sum_{m=1..(n+1)/2} ((2*m-1)^(n-2*m)*(-1)^(m-1))/(n-2*m+1)!.
a(n) ~ (n-1)! * sin(n*arctan(1/tan(r))) * (cos(r)/r)^n, where r = Im(LambertW(I)) = A305200 = 0.576412723031435283148289239887... is the root of the equation exp(r*tan(r))=cos(r)/r. - Vaclav Kotesovec, Jan 02 2014
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MATHEMATICA
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Rest[CoefficientList[Series[ArcTan[x*Exp[x]], {x, 0, 20}], x]*Range[0, 20]!] (* Vaclav Kotesovec, Jan 02 2014 *)
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PROG
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(Maxima)
a(n):=n!*sum(((2*m-1)^(n-2*m)*(-1)^(m-1))/(n-2*m+1)!, m, 1, (n+1)/2);
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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