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A191720
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Expansion of e.g.f. arctan(exp(x)-1).
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1
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1, 1, -1, -11, -25, 181, 2039, 3109, -131545, -1417259, 2734679, 239834629, 2217084935, -23659572299, -859070164681, -5378041927451, 198832696957415, 5164126517703061, 4868884057959959, -2309488856960067131
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n) = sum(m=1..(n+1)/2, ((-1)^(m-1)*(2*m-2)!*stirling2(n,2*m-1))).
a(n) ~ (n-1)! * 2^(2*n) * sin(n*arctan(Pi/log(4))) / (Pi^2+4*log(2)^2)^(n/2). - Vaclav Kotesovec, Jan 02 2014
a(n) = (-1)^(n+1)*Im(Li_{1-n}(1+i)), where Li_n(x) is the polylogarithm, i=sqrt(-1). - Vladimir Reshetnikov, Oct 31 2015
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MAPLE
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a:=series(arctan(exp(x)-1), x=0, 21): seq(n!*coeff(a, x, n), n=0..20); # Paolo P. Lava, Mar 27 2019
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MATHEMATICA
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nn=20; Rest[CoefficientList[Series[ArcTan[Exp[x]-1], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 22 2011 *)
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PROG
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(Maxima)
a(n):=sum(((-1)^(m-1)*(2*m-2)!*stirling2(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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STATUS
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approved
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