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%I #13 Sep 08 2022 08:44:38
%S 1,0,0,0,12,-60,450,-2940,33488,-360864,4785480,-62142960,941944872,
%T -14815408608,260792820288,-4784515051680,95341465939968,
%U -1988764871186304,44407627224011712,-1038296963667026304
%N Expansion of e.g.f. sec(arcsin(x)*log(x+1)).
%H G. C. Greubel, <a href="/A012314/b012314.txt">Table of n, a(n) for n = 0..434</a>
%e E.g.f. = 1 + 12*x^4/4! - 60*x^5/5! + 450*x^6/6! - 2940*x^7/7! + ...
%p 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
%t With[{nn=30}, CoefficientList[Series[Sec[ArcSin[x]*Log[x+1]], {x,0,nn}],x]*Range[0, nn]!] (* _G. C. Greubel_, Oct 25 2018 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(1/cos(asin(x)*log(x+1)))) \\ _G. C. Greubel_, Oct 25 2018
%o (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
%K sign
%O 0,5
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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