%I #17 Sep 08 2022 08:44:38

%S 0,0,2,-3,12,-40,358,-2499,25032,-229104,2865402,-36173115,550240020,

%T -8500522680,149846317710,-2762418635235,56365118364240,

%U -1205267403147360,27829436319559410,-674568212738977395

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

%H G. C. Greubel, <a href="/A012305/b012305.txt">Table of n, a(n) for n = 0..426</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)*arcsin(arcsin(x)*log(x+1)),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Oct 25 2018

%t With[{nn=20},Drop[CoefficientList[Series[ArcSin[ArcSin[x]Log[x+1]],{x,0,nn}],x] Range[0,nn]!,2]] (* _Harvey P. Dale_, Oct 18 2013 *)

%o (PARI) x='x+O('x^30); concat([0,0], Vec(serlaplace(asin(asin(x)* log(x+1))))) \\ _G. C. Greubel_, Oct 25 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Arcsin(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