A369698 AGM transform of positive cubes.

0, 49, 40824, 96461056, 571250390625, 7338413252698641, 181953686508203782144, 7957561391610438862503936, 572547082070592542500791107625, 64157961305703333114506988525390625, 10714350425499230222239742740718898118656, 2571996060859292513876561308464753498396819456

Offset

1,2

Comments

See A368366 for the description of the AGM transform.

Links

Paolo Xausa, Table of n, a(n) for n = 1..120

Formula

a(n) = A000537(n)^n - A000312(n)*A000442(n).

Mathematica

A369698[n_] := (n*(n+1)/2)^(2*n) - n^n*n!^3; Array[A369698, 15]

Prog

(Python)
from math import factorial
def A369698(n): return ((n*(n+1))**(m:=n<<1)>>m) - n**n*factorial(n)**3 # Chai Wah Wu, Jan 29 2024

Crossrefs

Cf. A368366, A368368.

Cf. A000312, A000442, A000537.

Sequence in context: A210819 A173171 A100418 * A351443 A239169 A395609

Adjacent sequences: A369695 A369696 A369697 * A369699 A369700 A369701

Keyword

nonn

Author

Paolo Xausa, Jan 29 2024

Status

approved