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A152915 Exponacci (or exponential Fibonacci) numbers.

%I A152915 #22 Oct 22 2024 20:48:23
%S A152915 1,1,2,9,64,3125,1679616,96889010407,9223372036854775808,
%T A152915 278128389443693511257285776231761,
%U A152915 10000000000000000000000000000000000000000000000000000000
%N A152915 Exponacci (or exponential Fibonacci) numbers.
%H A152915 Alois P. Heinz, <a href="/A152915/b152915.txt">Table of n, a(n) for n = 0..15</a>
%H A152915 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fibonacci_number">Fibonacci number</a>
%F A152915 a(0) = 1, a(n) = n ^ Fibonacci(n) for n > 0; Fibonacci = A000045.
%e A152915 a(9) = 9 ^ Fibonacci(9) = 9 ^ 34 = 278128389443693511257285776231761.
%p A152915 a:= n-> n^(<<1|1>, <1|0>>^n)[1, 2]:
%p A152915 seq(a(n), n=0..12);  # _Alois P. Heinz_, Jun 17 2014
%t A152915 Array[ #^Fibonacci[ # ]&,12] (* _Vladimir Joseph Stephan Orlovsky_, Apr 03 2010 *)
%o A152915 (Other) unsigned long Exponacci(unsigned int n)
%o A152915 {
%o A152915 if (n == 0)
%o A152915 return 1;
%o A152915 return pow(n, Fibonacci(n));
%o A152915 }
%o A152915 (Magma) [n^Fibonacci(n): n in [1..10]]; // _Vincenzo Librandi_, Apr 05 2017
%Y A152915 Cf. A000045, A100399.
%Y A152915 Main diagonal of A244003.
%K A152915 nonn
%O A152915 0,3
%A A152915 ShaoJun Ying (dolphinysj(AT)gmail.com), Dec 15 2008
%E A152915 More terms from _Vladimir Joseph Stephan Orlovsky_, Apr 03 2010