A201615 -id:A201615 - cp's OEIS frontend

A100399 a(n) = Fibonacci(n)^n.

1, 1, 1, 8, 81, 3125, 262144, 62748517, 37822859361, 60716992766464, 253295162119140625, 2775173073766990340489, 79496847203390844133441536, 5965226978431093156430190442313, 1171598758708107367475386427203165009, 602486784535040403801858901000000000000000

Offset: 0

Jorge Coveiro, Dec 30 2004

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..50

Main diagonal of A103323.

Cf. A000045, A067961, A152915, A201615, A201616.

[Fibonacci(n)^n: n in [0..20]]; // Vincenzo Librandi, Apr 24 2011

a:= n-> (<<1|1>, <1|0>>^n)[1, 2]^n:
seq(a(n), n=0..15);  # Alois P. Heinz, Apr 13 2018

Array[Fibonacci[ # ]^#&,20] (* Vladimir Joseph Stephan Orlovsky, Apr 03 2010 *)

PARI
```
a(n) = fibonacci(n)^n;
```

a(n) = A103323(n,n).
From Amiram Eldar, Nov 17 2020: (Start)
Sum_{n>=1} 1/a(n) = A201615.
Sum_{n>=1} (-1)^(n+1)/a(n) = A201616. (End)

A201616 Decimal expansion of Sum_{n = 1 .. infinity} (-1)^(n+1)/F(n)^n where F=A000045 is the Fibonacci sequence.

Original entry on oeis.org

1, 1, 2, 9, 7, 0, 5, 2, 2, 2, 0, 0, 5, 9, 7, 7, 4, 2, 2, 3, 8, 0, 4, 0, 6, 7, 7, 9, 0, 4, 2, 8, 7, 9, 4, 3, 4, 0, 8, 6, 1, 9, 1, 4, 5, 0, 2, 3, 1, 6, 4, 4, 8, 6, 2, 1, 1, 2, 1, 0, 5, 0, 7, 6, 7, 7, 7, 0, 1, 9, 5, 3, 8, 3, 2, 7, 3, 0, 7, 9, 8, 9, 2, 9, 2, 6, 3, 4, 6, 4, 8, 2, 2, 8, 9, 4, 3, 8, 9, 6, 9, 3, 7, 8, 8

Offset: 0

Michel Lagneau, Dec 03 2011

			0.1129705222005977422380406779... = 1/1^1 - 1/1^2 + 1/2^3 - 1/3^4 + 1/5^5 - ...

Cf. A079586, A158933, A000045, A201615.

with(combinat,fibonacci):Digits:=120:s:=sum( evalf(((-1)^(n+1))/ fibonacci(n)^n),n=1..200):print(s):

RealDigits[N[Sum[((-1)^(n+1))/Fibonacci[n]^n,{n,1,105}],105]][[1]]

-suminf(n=1,(-1)^n/fibonacci(n)^n) \\ Charles R Greathouse IV, Dec 05 2011

cp's OEIS Frontend

A100399 a(n) = Fibonacci(n)^n.

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