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 A066526 a(n) = binomial(Fibonacci(n), Fibonacci(n-1)). 4
 1, 1, 2, 3, 10, 56, 1287, 203490, 927983760, 841728816603675, 4404006643598438948468376, 26481463552095445860988385376871250071680, 1057375592689477481644154770179770478007054345083466115864070012050 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Harry J. Smith, Table of n, a(n) for n = 1..18 FORMULA Lim_{n->infinity} log(a(n))/log(a(n-1)) = phi. - Gerald McGarvey, Jul 25 2004 Lim_{n->infinity} log(a(n))/log(a(n-1)) = phi follows from Stirling's approximation and the approximation log(F(n)) = n log(phi) + O(1). In fact, log(a(n)) = K phi^n + O(n); the value of K does not matter for this result, but it is log(phi)/phi. - Franklin T. Adams-Watters, Dec 14 2006 a(n) ~ 5^(1/4) * phi^(3/2 - n/2 + phi^(n-1)) / sqrt(2*Pi), where phi = (1+sqrt(5))/2 = A001622. - Vaclav Kotesovec, Nov 13 2014 a(n) = A060001(n) / (A060001(n-1) * A060001(n-2)). - Vaclav Kotesovec, Nov 13 2014 EXAMPLE a(7) = binomial(Fibonacci(8), Fibonacci(7)) = binomial(21, 13) = 1287. MAPLE with(combinat): P:=proc(q) local n; for n from 1 to q do print(binomial(fibonacci(n), fibonacci(n-1))); od; end: P(20); # Paolo P. Lava, Feb 04 2015 MATHEMATICA Table[ Binomial[ Fibonacci[n], Fibonacci[n - 1]], {n, 1, 14} ] Binomial[Last[#], First[#]]&/@Partition[Fibonacci[Range[0, 15]], 2, 1] (* Harvey P. Dale, Oct 15 2014 *) PROG (PARI) { for (n=1, 18, a=binomial(fibonacci(n), fibonacci(n-1)); write("b066526.txt", n, " ", a) ) } \\ Harry J. Smith, Feb 21 2010 CROSSREFS Cf. A000045, A007318, A060001, A001622. Sequence in context: A192258 A052561 A181927 * A093856 A173097 A088221 Adjacent sequences:  A066523 A066524 A066525 * A066527 A066528 A066529 KEYWORD easy,nice,nonn AUTHOR Joe Faust, Jan 05 2002 EXTENSIONS Edited by Robert G. Wilson v, Jan 07 2002 Minor edits by Vaclav Kotesovec, Nov 13 2014 STATUS approved

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Last modified November 16 06:50 EST 2018. Contains 317258 sequences. (Running on oeis4.)