A067055 a(n) = (n!)^(n*(n+1)/2).

1, 1, 8, 46656, 63403380965376, 15407021574586368000000000000000, 1009212044656507725162109374628859215872000000000000000000000, 46564508204734663249790730337537405675293855389346558493242680777666577039360000000000000000000000000000

Offset

0,3

Links

Table of n, a(n) for n=0..7.

Formula

(Product of first n natural numbers )^(sum of first n natural numbers )

a(n) ~ (2*Pi)^(n*(n+1)/4) * n^(n*(n+1)*(2*n+1)/4) / exp((n+1)*(12*n^2 - 1)/24). - Vaclav Kotesovec, Apr 14 2023

Example

a(5) = (5!)^(1+...+5) = 120^15 = 15407021574586368000000000000000. a(6) = 720^21.

Maple

seq(mul(mul(j^k, j=1..n), k=1..n), n=0..7); # Zerinvary Lajos, Jun 02 2007

Mathematica

Table[n!^(n(n + 1)/2), {n, 1, 7}]

Prog

(PARI): for(n=1, 7, print1(n!^sum(k=1, n, k), ", "))

Crossrefs

Cf. A000142, A000217.

Sequence in context: A349113 A175855 A063374 * A137142 A368066 A036535

Adjacent sequences: A067052 A067053 A067054 * A067056 A067057 A067058

Keyword

easy,nonn

Author

Amarnath Murthy, Jan 02 2002

Extensions

More terms from Jason Earls and Robert G. Wilson v, Jan 04 2002

a(0)=1 prepended by Alois P. Heinz, Nov 13 2018

Status

approved