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Expansion of e.g.f. tan(arcsin(x) * log(x+1)).
1

%I #15 Sep 08 2022 08:44:38

%S 0,0,2,-3,12,-40,478,-3759,40152,-387864,4962042,-64308915,983170980,

%T -15335058960,267831905430,-4873619226735,96888423426480,

%U -2014804884605520,44917521867736050,-1047513682848869955

%N Expansion of e.g.f. tan(arcsin(x) * log(x+1)).

%H G. C. Greubel, <a href="/A012306/b012306.txt">Table of n, a(n) for n = 0..434</a>

%e E.g.f. = 2*x^2/2! - 3*x^3/3! + 12*x^4/4! - 40*x^5/5! + ...

%p seq(coeff(series(factorial(n)*tan(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[Tan[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); concat([0,0], Vec(serlaplace(tan(asin(x)* log(x+1))))) \\ _G. C. Greubel_, Oct 25 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Tan(Arcsin(x)*Log(x+1)) )); [0,0] cat [Factorial(n+1)*b[n]: n in [1..m-2]]; // _G. C. Greubel_, Oct 25 2018

%K sign

%O 0,3

%A Patrick Demichel (patrick.demichel(AT)hp.com)

%E a(0) and a(1) inserted and title improved by _Sean A. Irvine_, Jul 17 2018