A023813 a(n) = n^(n*(n+1)/2).

1, 1, 8, 729, 1048576, 30517578125, 21936950640377856, 459986536544739960976801, 324518553658426726783156020576256, 8727963568087712425891397479476727340041449, 10000000000000000000000000000000000000000000000000000000

Offset: 0

Author

Lyle Ramshaw (ramshaw(AT)pa.dec.com)

Keywords

• easy
• nonn

Comments

Determinant of n X n matrix M_(i,j) = binomial(n*i,j). - Benoit Cloitre, Sep 13 2003

Number of commutative binary operations on an n-set. Labeled commutative groupoids.

Links

• Eric Postpischil, Posting to sci.math newsgroup, May 21 1990
• Index entries for sequences related to groupoids

Crossrefs

a(n) + A079182(n) = A002489(n).

Cf. A000217, A001425, A002489, A023814, A023815.

Programs

Maple

seq(mul(n^k, k=1..n), n=0..10); # Zerinvary Lajos, Jun 03 2007

Mathematica

Table[n^((n^2 + n)/2), {n, 1, 10}]  (* Geoffrey Critzer, Jan 27 2013 *)

Formula

a(n) = Product_{k=1..n} n^k. - José de Jesús Camacho Medina, Jul 12 2016

a(n) = n^A000217(n). - Alois P. Heinz, Aug 06 2018

Extensions

Better description from Amarnath Murthy, Dec 29 2001