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%I #2 Mar 30 2012 18:37:20
%S 1,1,3,12,82,1350,97888,15395388,3754569984,3038160817708,
%T 10054063262475469,52672088781183258841,474423679267205966998406,
%U 20987531454245723696517676183,2606758801245041424971290635855234
%N G.f.: exp( Sum_{n>=1} (x^n/n)*[Sum_{k=0..[n/2]} A034807(n,k)^n] ), where A034807 is a triangle of Lucas polynomials.
%e G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 82*x^4 + 1350*x^5 +...
%e log(A(x)) = x + 5*x^2/2 + 28*x^3/3 + 273*x^4/4 + 6251*x^5/5 +...+ A171187(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))^m))+x*O(x^n)),n)}
%Y Cf. A171187, A034807, A156216.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Dec 13 2009
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