OFFSET
0,3
COMMENTS
Compare to g.f. of Fibonacci sequence: exp( Sum_{n>=1} A000204(n)*x^n/n ), where A000204 is the Lucas numbers.
More generally, if exp( Sum_{n>=1} C(n) * x^n/n ) equals a power series in x with integer coefficients, then exp( Sum_{n>=1} C(n)^n * x^n/n ) also equals a power series in x with integer coefficients (conjecture).
FORMULA
a(n) = (1/n)*Sum_{k=1..n} A000204(k)^k*a(n-k) for n>0, with a(0) = 1.
Logarithmic derivative forms A067961. [From Paul D. Hanna, Sep 13 2010]
EXAMPLE
G.f.: A(x) = 1 + x + 5*x^2 + 26*x^3 + 634*x^4 + 32928*x^5 + 5704263*x^6 +...
log(A(x)) = x + 3^2*x^2/2 + 4^3*x^3/3 + 7^4*x^4/4 + 11^5*x^5/5 + 18^6*x^6/6 +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, (fibonacci(m+1)+fibonacci(m-1))^m*x^m/m)+x*O(x^n)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 06 2009
STATUS
approved