OFFSET
0,2
COMMENTS
Given g.f. A(x), note that A(x)^(1/5) is not an integer series.
LINKS
Fung Lam, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (3, -1).
FORMULA
G.f.: (1+x)^7 / (1-3*x+x^2).
a(n) = 3*a(n-1) - a(n-2), n>=8. - Fung Lam, May 19 2014
EXAMPLE
G.f.: A(x) = 1 + 10*x + 50*x^2 + 175*x^3 + 510*x^4 + 1376*x^5 + 3625*x^6 + ...
where the logarithm begins:
log(A(x)) = 5*1*2*x + 5*0*3*x^2/2 + 5*1*5*x^3/3 + 5*1*8*x^4/4 + 5*2*13*x^5/5 + 5*3*21*x^6/6 + 5*5*34*x^7/7 + 5*8*55*x^8/8 + 5*13*89*x^9/9 + ...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, 5*fibonacci(m-2)*fibonacci(m+2) *x^m/m) +x*O(x^n)), n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 05 2014
STATUS
approved