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%I #2 Mar 30 2012 18:37:16
%S 1,1,4,21,186,2482,52431,1742069,92198200,7788221136,1053871857226,
%T 228795949744458,79812945269217967,44781474458725910347,
%U 40447360752560508229164,58848264986153917140728453
%N L.g.f.: exp(Sum_{n>=1} a(n)*x^n/n) = 1 + x*exp(Sum_{n>=1} Lucas(n)*a(n)*x^n/n) where Lucas(n) = A000204(n).
%F L.g.f.: exp(Sum_{n>=1} a(n)*x^n/n) = 1 + x*G(x) where G(x) = g.f. of A158257.
%F exp(Sum_{n>=1} a(n)*x^n/n) = (1 + Sum_{n>=1} Lucas(n)*a(n)*x^n) / (1 + Sum_{n>=1} (Lucas(n)-1)*a(n)*x^n).
%e L.g.f.: A(x) = x + x^2/2 + 4*x^3/3 + 21*x^4/4 + 186*x^5/5 + 2482*x^6/6 +...
%e exp(A(x)) = 1 + x + x^2 + 2*x^3 + 7*x^4 + 44*x^5 + 458*x^6 + 7953*x^7 +...
%e exp(A(x)) = 1 + x*G(x) where G(x) is the g.f. of A158257 such that:
%e log(G(x)) = x + 3*1*x^2/2 + 4*4*x^3/3 + 7*21*x^4/4 + 11*186*x^5/5 + 18*2482*x^6/6 +...
%o (PARI) {a(n)=local(A=x+x^2);if(n==0,1,for(i=1,n-1,A=log(1+x*exp(sum(m=1,n,(fibonacci(m-1)+fibonacci(m+1))*x^m*polcoeff(A+x*O(x^m),m) )+x*O(x^n))));n*polcoeff(A,n))}
%Y Cf. A158257, A158108 (variant), A000204 (Lucas).
%K nonn
%O 0,3
%A _Paul D. Hanna_, Mar 28 2009
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