A368370 AGM transform of triangular numbers.

0, 4, 514, 113920, 44084375, 28195584256, 28201577788944, 42039291307622400, 89651019067859485125, 264184676314240000000000, 1044528435971290465713291136, 5403748103160416506028643844096, 35801791315095649217787108688094375

Offset: 1

Author

N. J. A. Sloane, Jan 24 2024

Keywords

• nonn

Comments

See A368366 for further information.

Crossrefs

Cf. A000217, A368366.

Programs

Mathematica

Table[Sum[k*(k+1)/2, {k, 1, n}]^n - n^n*Product[k*(k+1)/2, {k, 1, n}], {n, 1, 12}] (* Vaclav Kotesovec, Jan 24 2024 *)

Python

from math import comb, factorial
def A368370(n): return comb(n+2,3)**n-(n**n*factorial(n)**2*(n+1)>>n) # Chai Wah Wu, Jan 25 2024

Formula

a(n) ~ (n*(n+1)*(n+2)/6)^n - n^n*n!*(n+1)!/2^n. - Vaclav Kotesovec, Jan 24 2024