A370223 AGM transform of the positive Fibonacci numbers.

0, 0, 10, 865, 155082, 52802560, 40048988817, 71202718146816, 315615332953930528, 3574469013941010577249, 104798469697184132865547168, 7984603919946049180938300030976, 1584983603576817306123611193840098529, 820874582413458038007335015822715588591616

Offset: 1

Author

Paolo Xausa, Feb 13 2024

Keywords

• nonn

Comments

See A368366 for the description of the AGM transform.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..68

Crossrefs

Cf. A368366.

Cf. A000045, A000071, A000312, A003266.

Programs

Mathematica

A370223[n_] := (Fibonacci[n+2]-1)^n - n^n*Fibonorial[n]; Array[A370223, 15]

Python

from itertools import count, islice
def A370223_gen(): # generator of terms
    a, b, s, p = 1, 1, 0, 1
    for n in count(1):
        s += a
        p *= a
        yield s**n-n**n*p
        a, b = b, a+b
A370223_list = list(islice(A370223_gen(),10)) # Chai Wah Wu, Feb 16 2024

Formula

a(n) = A000071(n+2)^n - A000312(n)*A003266(n).