A368370 AGM transform of triangular numbers.

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

Offset

1,2

Comments

See A368366 for further information.

Links

Table of n, a(n) for n=1..13.

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A000217, A368366.

Sequence in context: A278878 A348703 A291830 * A003393 A089668 A257922

Adjacent sequences: A368367 A368368 A368369 * A368371 A368372 A368373

Keyword

nonn

Author

N. J. A. Sloane, Jan 24 2024

Status

approved