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%I #9 Mar 27 2019 03:49:45
%S 0,1,-1,3,-12,68,-480,4144,-42112,494360,-6581880,98079696,
%T -1617373296,29245459176,-575367843960,12235339942344,
%U -279650131845120,6836254328079936,-177979145883651648,4916243253642325056,-143602294106947553280,4422411460743707222784
%N Expansion of e.g.f. arcsin(log(1 + x)).
%F a(n) ~ -(-1)^n * n^(n-1) / (exp(1) - 1)^(n - 1/2). - _Vaclav Kotesovec_, Mar 26 2019
%e arcsin(log(1 + x)) = x^1/1! - x^2/2! + 3*x^3/3! - 12*x^4/4! + 68*x^5/5! - 480*x^6/6! + ...
%p a:=series(arcsin(log(1+x)),x=0,22): seq(n!*coeff(a,x,n),n=0..21); # _Paolo P. Lava_, Mar 26 2019
%t nmax = 21; CoefficientList[Series[ArcSin[Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 21; CoefficientList[Series[-I Log[I Log[1 + x] + Sqrt[1 - Log[1 + x]^2]], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A001710, A001818, A003703, A003708, A009024, A009454, A009775, A104150, A189815, A296980, A296981, A296982.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Dec 22 2017
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