%I #19 Jun 02 2017 20:10:40
%S 1,1,2,12,106,1330,21188,412496,9471180,250752012,7519114872,
%T 251898595344,9324409750104,377947150828728,16648683024776112,
%U 791945577071452608,40457530872588060816,2209174906291706917008,128405210614917271843872,7915238091104410779024576
%N E.g.f. exp((1-sqrt(1-4*log(1+x)))/2).
%H Vincenzo Librandi, <a href="/A184975/b184975.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = Sum_{k=1..n} (Sum_{i=0..(n-k)} ((i+k-1)!*C(k+2*i-1,i+k-1) *stirling1(n, i+k))))/(k-1)!), n>0, a(0)=1.
%F a(n) ~ n^(n-1) / (sqrt(2)*exp(n-3/8)*(exp(1/4)-1)^(n-1/2)). - _Vaclav Kotesovec_, Jun 02 2013
%t CoefficientList[Series[Exp[(1-Sqrt[1-4*Log[1+x]])/2], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 02 2013 *)
%o (Maxima) a(n):=if n=0 then 1 else sum((sum(((i+k-1)!*binomial(k+2*i-1,i+k-1) *stirling1(n,i+k)), i,0,n-k))/(k-1)!,k,1,n);
%o (PARI) x='x+O('x^50); Vec(serlaplace(exp((1-sqrt(1-4*log(1+x)))/2))) \\ _G. C. Greubel_, Jun 02 2017
%K nonn
%O 0,3
%A _Vladimir Kruchinin_, Nov 22 2011
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