OFFSET
0,3
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
EXAMPLE
G.f.: A(x) = 1 + x + 41*x^2 + 126*x^3 + 1526*x^4 + 7854*x^5 + 63629*x^6 +...
where
log(A(x)) = x + 3^4*x^2/2 + 4^4*x^3/3 + 7^4*x^4/4 + 11^4*x^5/5 + 18^4*x^6/6 + 29^4*x^7/7 + 47^4*x^8/8 +...+ Lucas(n)^4*x^n/n +...
MATHEMATICA
CoefficientList[Series[1/((1 - x)^6*(1 + 3*x + x^2)^4*(1 - 7*x + x^2)), {x, 0, 50}], x] (* G. C. Greubel, Dec 24 2017 *)
PROG
(PARI) /* Subroutine used in PARI programs below: */
{Lucas(n)=fibonacci(n-1)+fibonacci(n+1)}
(PARI) {a(n)=polcoeff(exp(sum(k=1, n, Lucas(k)^4*x^k/k)+x*O(x^n)), n)}
(PARI) {a(n, m=2)=polcoeff(1/(1 - (-1)^m*x+x*O(x^n))^binomial(2*m, m) * prod(k=1, m, 1/(1 - (-1)^(m-k)*Lucas(2*k)*x + x^2+x*O(x^n))^binomial(2*m, m-k)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 06 2012
STATUS
approved