%I #8 Sep 16 2024 23:59:05

%S 0,3,25,224,2073,19646,189267,1845115,18148809,179759988,1790426165,

%T 17914292003,179925732000,1812940879359,18317715471523,

%U 185522533906512,1882911883226921,19145400126464070,194989385131146079

%N a(n) = Sum_{k=0..n} F(n+k)*binomial(n+k,k) where F=A000045.

%C 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?

%t Table[Sum[Fibonacci[n+k]*Binomial[n+k,k],{k,0,n}],{n,0,18}] (* _James C. McMahon_, Sep 16 2024 *)

%o (PARI) a(n)=sum(k=0,n,binomial(n+k,k)*fibonacci(n+k))

%Y Cf. A000045.

%K nonn

%O 0,2

%A _Benoit Cloitre_, May 21 2006