OFFSET
0,3
COMMENTS
Compare to the g.f. of A054888.
Given g.f. A(x), note that A(x)^(1/5) is not an integer series.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,5,5,0,-1).
FORMULA
G.f.: 1 / ( (1-3*x+x^2) * (1+x)^3 ).
a(n) = (2*Lucas(2*n+5) + (28+25*n+5*n^2)*(-1)^(n))/50 where Lucas = A000032. - Greg Dresden, Jan 01 2021
EXAMPLE
G.f.: A(x) = 1 + 5*x^2 + 5*x^3 + 25*x^4 + 49*x^5 + 150*x^6 + 365*x^7 + ...
where the logarithm begins:
log(A(x)) = 5*1*2*x^2/2 + 5*1*3*x^3/3 + 5*2*5*x^4/4 + 5*3*8*x^5/5 + 5*5*13*x^6/6 + 5*8*21*x^7/7 + 5*13*34*x^8/8 + ...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, 5*fibonacci(m-1)*fibonacci(m+1)*x^m/m) + x*O(x^n)), n)}
for(n=0, 36, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 05 2014
STATUS
approved