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A297209
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Expansion of e.g.f. log(1 + arcsin(x))*exp(-x).
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3
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0, 1, -3, 9, -32, 148, -853, 6027, -49576, 470624, -5005137, 59454923, -774282632, 11035740844, -169997137269, 2826070412955, -50256453936368, 954657085889760, -19247168446169665, 411277539407862707, -9269937746437524256, 220085825544691181500, -5483977295221312280757
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OFFSET
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0,3
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LINKS
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EXAMPLE
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log(1 + arcsin(x))*exp(-x) = x/1! - 3*x^2/2! + 9*x^3/3! - 32*x^4/4! + 148*x^5/5! - 853*x^6/6! + ...
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MAPLE
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a:=series(log(1+arcsin(x))*exp(-x), x=0, 23): seq(n!*coeff(a, x, n), n=0..22); # Paolo P. Lava, Mar 26 2019
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MATHEMATICA
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nmax = 22; CoefficientList[Series[Log[1 + ArcSin[x]] Exp[-x], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 22; CoefficientList[Series[Log[1 - I Log[I x + Sqrt[1 - x^2]]] Exp[-x], {x, 0, nmax}], x] Range[0, nmax]!
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PROG
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(PARI) x='x+O('x^99); concat([0], Vec(serlaplace(exp(-x)*log(1+asin(x))))) \\ Altug Alkan, Dec 28 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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