The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #2 Mar 30 2012 18:37:20
%S 1,1,5,14,40,126,408,1332,4473,15377,53627,189724,680475,2467975,
%T 9038578,33399571,124400702,466619283,1761467038,6688059913,
%U 25527326897,97901917060,377123873505,1458573962761,5662223702216,22056563938599
%N G.f.: exp( Sum_{n>=1} (x^n/n)*[Sum_{k=0..[n/2]} A034807(n,k)^3] ), where A034807 is a triangle of Lucas polynomials.
%e G.f.: A(x) = 1 + x + 5*x^2 + 14*x^3 + 40*x^4 + 126*x^5 + 408*x^6 +...
%e log(A(x)) = x + 9*x^2/2 + 28*x^3/3 + 73*x^4/4 + 251*x^5/5 + 954*x^6/6 +...+ A171215(n)*x^n/n +...
%o (PARI) {a(n)=polcoeff(exp(sum(m=1,n,(x^m/m)*sum(k=0, m\2, (binomial(m-k, k)+binomial(m-k-1, k-1))^3))+x*O(x^n)),n)}
%Y Cf. A171215, A093128, A171186.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Dec 14 2009