|
|
A095917
|
|
Unreduced numerator of Sum[k=1..n, -(-1)^k/(F(k)*F(k+1))], with F(i) = A000045(i) the Fibonacci numbers.
|
|
1
|
|
|
1, 1, 8, 108, 4500, 460800, 126547200, 90150278400, 168726978201600, 825645617596800000, 10582810279847245440000, 355057327760217947504640000, 31189165230267027857184030720000, 7172521863132011354816602281246720000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Denominators are b(n) = Prod[k=1..n, F(k)*F(k+1)] and a(n)/b(n) approaches (sqrt(5)-1)/2.
Can a(n) be expressed in terms of F(n), without the sum? However, the sequence appears not to be C-finite.
|
|
LINKS
|
|
|
PROG
|
(PARI) a(n) = local(f, d, nu); f=sum(k=1, n, -(-1)^k*1 / fibonacci(k) / fibonacci(k+1)); d=denominator(f); nu=numerator(f); prod(k=1, n, fibonacci(k)*fibonacci(k+1))/d*nu
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|