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A158257 G.f.: A(x) = exp(Sum_{n>=1} Lucas(n)*L(n)*x^n/n) such that Sum_{n>=1} L(n)*x^n/n = log(1+x*A(x)) where L(n) = A158258(n) and Lucas(n) = A000204(n). 2

%I #2 Mar 30 2012 18:37:16

%S 1,1,2,7,44,458,7953,225761,10470604,789302962,96596105976,

%T 19162936947418,6158621106553275,3204835468356347519,

%U 2699695571885775547222,3680716263445262350996413

%N G.f.: A(x) = exp(Sum_{n>=1} Lucas(n)*L(n)*x^n/n) such that Sum_{n>=1} L(n)*x^n/n = log(1+x*A(x)) where L(n) = A158258(n) and Lucas(n) = A000204(n).

%e G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 44*x^4 + 458*x^5 + 7953*x^6 +...

%e log(1+x*A(x)) = x + x^2/2 + 4*x^3/3 + 21*x^4/4 + 186*x^5/5 + 2482*x^6/6 +...

%e log(A(x)) = x + 3*x^2/2 + 16*x^3/3 + 147*x^4/4 + 2046*x^5/5 + 44676*x^6/6 +...

%e log(A(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=1+x);if(n==0,1,for(i=1,n,A=exp(sum(m=1,n,(fibonacci(m-1)+fibonacci(m+1))*x^m*polcoeff(log(1+x*A+x*O(x^m)),m))+x*O(x^n)));polcoeff(A,n))}

%Y Cf. A158258, A158107 (variant), A000204 (Lucas).

%K nonn

%O 0,3

%A _Paul D. Hanna_, Mar 28 2009

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