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%I #9 Jan 30 2020 21:29:17
%S 0,1,3,10,27,76,210,589,1659,4708,13428,38479,110682,319411,924339,
%T 2681410,7794939,22702396,66229212,193495279,566069052,1658026093,
%U 4861703289,14269842184,41922504570,123265254451,362719839225,1068105234304
%N a(n) = n*Sum_{i=0..n-1} binomial(n,i)*binomial(i-1,n-i-1)/(n-i).
%F G.f.: (3*x^3+sqrt(-3*x^2-2*x+1)*(x^2+4*x-3)-3*x^2-7*x+3)/(sqrt(-3*x^2-2*x+1)*(2*x^3-x^2-2*x+1)-3*x^3+x^2+3*x-1).
%F D-finite with recurrence: +n*a(n) +(-3*n+2)*a(n-1) +2*(-n+1)*a(n-2) +2*(3*n-7)*a(n-3) +(n-2)*a(n-4) +3*(-n+4)*a(n-5)=0. - _R. J. Mathar_, Mar 12 2017
%o (Maxima)
%o (3*x^3+sqrt(-3*x^2-2*x+1)*(x^2+4*x-3)-3*x^2-7*x+3)/(sqrt(-3*x^2-2*x+1)*(2*x^3-x^2-2*x+1)-3*x^3+x^2+3*x-1);
%o taylor(%,x,0,27);
%K nonn
%O 0,3
%A _Vladimir Kruchinin_, Dec 06 2016
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