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A118726
a(n) = Sum_{k=0..n} F(n+k)*binomial(n+k,k) where F=A000045.
0
0, 3, 25, 224, 2073, 19646, 189267, 1845115, 18148809, 179759988, 1790426165, 17914292003, 179925732000, 1812940879359, 18317715471523, 185522533906512, 1882911883226921, 19145400126464070, 194989385131146079
OFFSET
0,2
COMMENTS
If (2n+1)>5 is not divisible by 5 and (2n+1) divides a(n) then (2n+1) is often prime. What is the set of exceptions?
MATHEMATICA
Table[Sum[Fibonacci[n+k]*Binomial[n+k, k], {k, 0, n}], {n, 0, 18}] (* James C. McMahon, Sep 16 2024 *)
PROG
(PARI) a(n)=sum(k=0, n, binomial(n+k, k)*fibonacci(n+k))
CROSSREFS
Cf. A000045.
Sequence in context: A370104 A024217 A199679 * A372458 A066221 A370280
KEYWORD
nonn
AUTHOR
Benoit Cloitre, May 21 2006
STATUS
approved