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A191719 E.g.f. arctan(x*exp(x)) 4
1, 2, 1, -20, -151, -354, 6217, 100472, 537777, -7631270, -223395919, -2120164188, 22050300505, 1154262915638, 17130776734905, -105423782758544, -11372993234072863, -245877012220234446, 345837436238423521, 188329590656514108380 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..20.

FORMULA

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)) = 0.576412723031435283148289239887... is the root of the equation exp(r*tan(r))=cos(r)/r. - Vaclav Kotesovec, Jan 02 2014

MATHEMATICA

Rest[CoefficientList[Series[ArcTan[x*Exp[x]], {x, 0, 20}], x]*Range[0, 20]!] (* Vaclav Kotesovec, Jan 02 2014 *)

PROG

(Maxima)

a(n):=n!*sum(((2*m-1)^(n-2*m)*(-1)^(m-1))/(n-2*m+1)!, m, 1, (n+1)/2);

CROSSREFS

Sequence in context: A013158 A012932 A013163 * A009768 A051492 A164827

Adjacent sequences:  A191716 A191717 A191718 * A191720 A191721 A191722

KEYWORD

sign

AUTHOR

Vladimir Kruchinin, Jun 13 2011

STATUS

approved

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Last modified February 24 05:37 EST 2018. Contains 299597 sequences. (Running on oeis4.)