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A012314
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Expansion of e.g.f. sec(arcsin(x)*log(x+1)).
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1
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1, 0, 0, 0, 12, -60, 450, -2940, 33488, -360864, 4785480, -62142960, 941944872, -14815408608, 260792820288, -4784515051680, 95341465939968, -1988764871186304, 44407627224011712, -1038296963667026304
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OFFSET
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0,5
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LINKS
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EXAMPLE
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E.g.f. = 1 + 12*x^4/4! - 60*x^5/5! + 450*x^6/6! - 2940*x^7/7! + ...
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MAPLE
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seq(coeff(series(factorial(n)*sec(arcsin(x)*log(x+1)), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 25 2018
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MATHEMATICA
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With[{nn=30}, CoefficientList[Series[Sec[ArcSin[x]*Log[x+1]], {x, 0, nn}], x]*Range[0, nn]!] (* G. C. Greubel, Oct 25 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(1/cos(asin(x)*log(x+1)))) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 1/Cos(Arcsin(x)*Log(x+1)) )); [Factorial(n-1)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 25 2018
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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Patrick Demichel (patrick.demichel(AT)hp.com)
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STATUS
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approved
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