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A296438
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Expansion of e.g.f. log(1 + arctan(x))*exp(x).
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5
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0, 1, 1, 0, 0, 13, 5, -336, -56, 18593, -6735, -1598520, 1192664, 205475645, -255011835, -36324220856, 62049925040, 8519764352097, -18835422533375, -2551646722754512, 6927586371061712, 951619735931190157, -3077560879933239899, -432185107142832520576, 1624964470900980885432
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OFFSET
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0,6
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LINKS
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FORMULA
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E.g.f.: log(1 + i*(log(1 - i*x) - log(1 + i*x))/2)*exp(x), where i is the imaginary unit.
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EXAMPLE
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E.g.f.: A(x) = x/1! + x^2/2! + 13*x^5/5! + 5*x^6/6! - 336*x^7/7! - 56*x^8/8! + ...
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MAPLE
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a:=series(log(1+arctan(x))*exp(x), x=0, 25): seq(n!*coeff(a, x, n), n=0..24); # Paolo P. Lava, Mar 27 2019
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MATHEMATICA
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nmax = 24; CoefficientList[Series[Log[1 + ArcTan[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 24; CoefficientList[Series[Log[1 + I (Log[1 - I x] - Log[1 + I x])/2] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
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PROG
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(PARI) my(ox=O(x^30)); Vecrev(Pol(serlaplace(log(1 + atan(x + ox)) * exp(x + ox)))) \\ Andrew Howroyd, Dec 12 2017
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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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