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A049215
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Scaled coefficients of (arctanh x)^4.
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3
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1, 40, 2464, 229760, 30633856, 5561407488, 1322489954304, 399463775797248, 149519094622027776, 67960463478175825920, 36884466463352967659520, 23566236397584291201024000, 17511732541318788803985408000
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OFFSET
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0,2
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LINKS
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FORMULA
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E.g.f.: (arctanh x)^4 or (1-x^2)^-1 * (arctanh x)^3.
a(n) is coefficient of x^(2*n+4) in (arctanh x)^4, multiplied by (2*n+4)!/4!.
a(n) = (1/8) * Sum_{p=1..2*n+3} binomial(2*n+2,p-1)*Sum_{m=4..2*n+4} binomial(m,4)*abs(s(2*n+4,m))*((-p)^(m-4)+(-p)^(m-4)) where s(n,m) is Stirling number of first kind . - Ammar Khatab, Aug 13 2024
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EXAMPLE
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(arctanh x)^4 = x^4 + 4/3*x^6 + 22/15*x^8 + 1436/945*x^10 + ...
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MATHEMATICA
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a[n_] := SeriesCoefficient[ArcTanh[x]^4, {x, 0, 2n+4}]*(2n+4)!/4!;
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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Joe Keane (jgk(AT)jgk.org)
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STATUS
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approved
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