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

%I #14 Sep 08 2022 08:44:38

%S 1,0,2,-3,24,-100,808,-5439,51800,-469008,5292162,-59508075,782885532,

%T -10464052248,157781733198,-2437533390915,41504137389648,

%U -726658147836384,13799849799221682,-269818493378847219

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

%H G. C. Greubel, <a href="/A012304/b012304.txt">Table of n, a(n) for n = 0..448</a>

%e E.g.f. = 1 + 2*x^2/2! - 3*x^3/3! + 24*x^4/4! - 100*x^5/5! + ...

%p seq(coeff(series(factorial(n)*exp(arcsin(x)*log(x+1)),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Oct 26 2018

%t With[{nn=20},CoefficientList[Series[Exp[ArcSin[x]Log[x+1]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, May 27 2017 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(asin(x)*log(x+1)))) \\ _G. C. Greubel_, Oct 25 2018

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

%K sign

%O 0,3

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

%E Definition clarified by _Harvey P. Dale_, May 27 2017