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%I #10 Mar 31 2012 10:23:14
%S 1,1,1,1,3,7,15,33,93,309,1071,3699,13947,58293,260337,1202121,
%T 5797035,29682639,161252631,915546969,5401610901,33227826669,
%U 213648580503,1430820925083,9936454523427
%N E.g.f. A(x) satisfies differential equation A'''(x)=A(x)+A(x)^2, A(0)=0, A'(0)=1, A''(0)=1, A'''(0)=1.
%F a(n)=n!*b(n), b(n)=1/(n*(n-1)*(n-2))*(i=1..n-4, b(n-3)+sum(b(i)*b(n-3-i))), n>3, b(1)=1, b(2)=1/2, b(3)=1/6.
%o (Maxima)
%o a(n):=if n<4 then 1/n! else 1/(n*(n-1)*(n-2))*(a(n-3)+sum(a(i)*a(n-3-i),i,1,n-4));
%o makelist(n!*a3(n),n,1,25);
%K nonn
%O 1,5
%A _Vladimir Kruchinin_, Nov 18 2011
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