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A296730
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Expansion of e.g.f. arctanh(x*cos(x)) (odd powers only).
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4
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1, -1, -31, -337, 24705, 2451679, -17936543, -42895630065, -5396647099903, 1239561882325439, 708575518706816481, 37448619025871342959, -113842057082636742446975, -52054011876398495316250977, 16226448322449614832534708065, 31975745831751940004484917311439
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = (2*n+1)! * [x^(2*n+1)] arctanh(x*cos(x)).
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EXAMPLE
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arctanh(x*cos(x)) = x/1! - x^3/3! - 31*x^5/5! - 337*x^7/7! + 24705*x^9/9! + ...
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MATHEMATICA
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nmax = 16; Table[(CoefficientList[Series[ArcTanh[x Cos[x]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]
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PROG
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(PARI) first(n) = x='x+O('x^(2*n)); vecextract(Vec(serlaplace(atanh(x*cos(x)))), (4^n - 1)/3) \\ Iain Fox, Dec 19 2017
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CROSSREFS
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Cf. A000364, A009015, A009016, A009446, A009447, A009633, A009634, A010050, A012494, A191512, A296465, A296467, A296728, A296729, A296731, A296740.
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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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