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%I #2 Mar 30 2012 18:37:17
%S 1,1,2,5,14,40,159,812,5133,42942,474619,6708142,121367878,2819170132,
%T 83571532538,3148951107867,151069353323782,9219463980803329,
%U 714951048370178409,70448496563603216429,8818161368662624534857
%N G.f.: A(x) = exp( Sum_{n>=1} (1 + A000204(n)*x)^n * x^n/n ).
%C Compare to g.f. of Fibonacci sequence: exp( Sum_{n>=1} A000204(n)*x^n/n ), where A000204 is the Lucas numbers.
%e G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 40*x^5 + 159*x^6 +...
%o (PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, (1+(fibonacci(m-1)+fibonacci(m+1))*x+x*O(x^n))^m*x^m/m)), n)}
%Y Cf. A156216, A156100, A159308, A000204.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jul 22 2009
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