OFFSET
0,3
COMMENTS
LINKS
Robert Israel, Table of n, a(n) for n = 0..3000
FORMULA
EXAMPLE
G.f.: A(x) = 1 + x + 5*x^2 + 10*x^3 + 30*x^4 + 63*x^5 + 170*x^6 + 355*x^7 + ...
log(A(x)) = x + 3*3*x^2/2 + 4*4*x^3/3 + 7*7*x^4/4 + 6*11*x^5/5 + 12*18*x^6/6 + ...
Also, the g.f. equals the product:
A(x) = 1/((1-x-x^2) * (1-3*x^2+x^4) * (1-4*x^3-x^6) * (1-7*x^4+x^8) * (1-11*x^5-x^10) * (1-18*x^6+x^12) * ... * (1 - Lucas(n)*x^n + (-1)^n*x^(2*n)) * ...).
MAPLE
N:= 100: # to get a(0) to a(N)
G:= exp(add(numtheory:-sigma(n)*lucas(n)*x^n/n, n=1..N)):
S:= series(G, x, N+1):
seq(coeff(S, x, i), i=0..N); # Robert Israel, Dec 23 2015
PROG
(PARI) {a(n)=polcoeff(exp(sum(k=1, n, sigma(k)*(fibonacci(k-1)+fibonacci(k+1))*x^k/k)+x*O(x^n)), n)}
for(n=0, 40, print1(a(n), ", "))
(PARI) {Lucas(n)=fibonacci(n-1)+fibonacci(n+1)}
{a(n)=polcoeff(prod(m=1, n, 1/(1-Lucas(m)*x^m+(-1)^m*x^(2*m)+x*O(x^n))), n)}
for(n=0, 40, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 06 2009
STATUS
approved