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%I #12 May 25 2017 03:20:02
%S 1,1,8,64,824,12968,252720,5789712,153169440,4589004192,153643615872,
%T 5684390364288,230307823878144,10141452865049088,482259966649655808,
%U 24630247225278881280,1344614199041549399040,78137673004382654223360
%N Expansion of (1-sqrt(1-4*log(1+x)))/2.
%H G. C. Greubel, <a href="/A087138/b087138.txt">Table of n, a(n) for n = 1..372</a>
%F a(n) = Sum_{k=1..n} Stirling1(n, k)*k!*Catalan(k-1).
%F a(n) ~ n! / (2*exp(1/8)*sqrt(Pi) * (exp(1/4)-1)^(n-1/2) * n^(3/2)). - _Vaclav Kotesovec_, May 03 2015
%t Rest[CoefficientList[Series[(1-Sqrt[1-4*Log[1+x]])/2, {x, 0, 20}], x] * Range[0, 20]!] (* _Vaclav Kotesovec_, May 03 2015 *)
%o (PARI) x='x+O('x^50); Vec(serlaplace((1-sqrt(1-4*log(1+x)))/2)) \\ _G. C. Greubel_, May 24 2017
%Y Cf. A000108, A052851, A052803, A052886, A052895, A006531, A048287.
%K nonn
%O 1,3
%A _Vladeta Jovovic_, Oct 18 2003
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