OFFSET
0,3
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..60
Sawian Jaidee, Patrick Moss, Tom Ward, Time-changes preserving zeta functions, arXiv:1809.09199 [math.DS], 2018.
FORMULA
a(n) = (1/n)*Sum_{k=1..n} Lucas(k^2)*a(n-k), a(0)=1.
Logarithmic derivative yields A166169.
EXAMPLE
G.f.: A(x) = 1 + x + 4*x^2 + 29*x^3 + 585*x^4 + 34212*x^5 +...
log(A(x)) = x + 7*x^2/2 + 76*x^3/3 + 2207*x^4/4 + 167761*x^5/5 + 33385282*x^6/6 +...+ Lucas(n^2)*x^n/n +...
MAPLE
with(combinat): seq(coeff(series(exp(add((fibonacci(k^2-1)+fibonacci(k^2+1))*x^k/k, k=1..n)), x, n+1), x, n), n = 0 .. 15); # Muniru A Asiru, Dec 18 2018
MATHEMATICA
CoefficientList[Series[Exp[Sum[LucasL[n^2]*x^n/n, {n, 1, 200}]], {x, 0, 50}], x](* G. C. Greubel, May 06 2016 *)
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, (fibonacci(m^2-1)+fibonacci(m^2+1))*x^m/m)+x*O(x^n)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 08 2009
STATUS
approved