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).

1, 1, 2, 7, 44, 458, 7953, 225761, 10470604, 789302962, 96596105976, 19162936947418, 6158621106553275, 3204835468356347519, 2699695571885775547222, 3680716263445262350996413

Offset: 0

Author

Paul D. Hanna, Mar 28 2009

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 44*x^4 + 458*x^5 + 7953*x^6 +...
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 +...
log(A(x)) = x + 3*x^2/2 + 16*x^3/3 + 147*x^4/4 + 2046*x^5/5 + 44676*x^6/6 +...
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 +...
		

Crossrefs

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

Programs

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))}