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%I #14 Sep 08 2022 08:44:38
%S 1,1,3,6,53,235,2709,20188,278249,3019693,48281695,692436338,
%T 12717929157,225943945071,4727712830281,99660715587704,
%U 2354596166060273,57197420701626009,1511830772603161339
%N Expansion of e.g.f. arcsin(exp(x)*log(x+1)).
%H G. C. Greubel, <a href="/A012275/b012275.txt">Table of n, a(n) for n = 0..421</a>
%e E.g.f. = x + x^2/2! + 3*x^3/3! + 6*x^4/4! + 53*x^5/5! + ...
%p seq(coeff(series(factorial(n)*arcsin(exp(x)*log(x+1)),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Oct 28 2018
%t With[{nn = 30}, CoefficientList[Series[ArcSin[Exp[x]*Log[x+1]], {x, 0, nn}], x] Range[0, nn]!] (* _G. C. Greubel_, Oct 28 2018 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(asin(exp(x)*log(x+1)))) \\ _G. C. Greubel_, Oct 28 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Arcsin(Exp(x)*Log(x+1)) )); [Factorial(n)*b[n]: n in [1..m-1]]; // _G. C. Greubel_, Oct 28 2018
%K nonn
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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