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A205505 Fibonacci(n*(n+1)) / Fibonacci(n). 1

%I

%S 1,8,72,2255,166408,33489287,17373187209,23735905327584,

%T 84707858657965180,792123204706451722511,19386236394149894806708656,

%U 1242293991563772001787883943693,208405704482555536994509895576090977,91533085042008706066658193727853843719640

%N Fibonacci(n*(n+1)) / Fibonacci(n).

%F a(n) = [x^n] 1/(1 - Lucas(n)*x + (-1)^n*x^2), where Lucas(n) = A000204(n).

%F Forms a diagonal in table A028412.

%t Table[Fibonacci[n(n+1)]/Fibonacci[n],{n,20}] (* _Harvey P. Dale_, Mar 30 2012 *)

%o (PARI) {a(n)=fibonacci(n*(n+1))/fibonacci(n)}

%o (PARI) {Lucas(n)=fibonacci(n-1)+fibonacci(n+1)}

%o {a(n)=polcoeff(1/(1-Lucas(n)*x+(-1)^n*x^2+x*O(x^n)), n)}

%Y Cf. A103624, A051294, A028412.

%K nonn,easy

%O 1,2

%A _Paul D. Hanna_, Jan 28 2012

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Last modified September 27 10:35 EDT 2020. Contains 337380 sequences. (Running on oeis4.)