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%I #15 Sep 08 2022 08:44:38
%S 0,1,2,5,20,133,1070,10705,125512,1717321,26518138,459336605,
%T 8787628060,184388779469,4205082557286,103631769297641,
%U 2743399950572304,77654985344871313,2340183966373322610
%N Expansion of e.g.f. arcsin(arcsin(x) * exp(x)).
%H Robert Israel, <a href="/A012317/b012317.txt">Table of n, a(n) for n = 0..410</a>
%e E.g.f. = x + 2/2!*x^2 + 5/3!*x^3 + 20/4!*x^4 + 133/5!*x^5 ...
%p S:= series(arcsin(arcsin(x)*exp(x)),x,51):
%p seq(coeff(S,x,j)*j!,j=0..50); # _Robert Israel_, Oct 25 2018
%t With[{nmax = 30}, CoefficientList[Series[ArcSin[ArcSin[x]*Exp[x]], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Oct 25 2018 *)
%o (PARI) x='x+O('x^30); concat([0], Vec(serlaplace( asin(asin(x)*exp(x))))) \\ _G. C. Greubel_, Oct 25 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Arcsin(Arcsin(x)*Exp(x)))); [0] cat [Factorial(n)*b[n]: n in [1..m-1]]; // _G. C. Greubel_, Oct 25 2018
%K nonn
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E a(0) inserted and title improved by _Sean A. Irvine_, Jul 17 2018
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