A369698 AGM transform of positive cubes.

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

Offset: 1

Author

Paolo Xausa, Jan 29 2024

Keywords

• nonn

Comments

See A368366 for the description of the AGM transform.

Links

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

Crossrefs

Cf. A368366, A368368.

Cf. A000312, A000442, A000537.

Programs

Mathematica

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

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

Formula

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