A118542 Number of nonisomorphic groupoids with <= n elements.

1, 2, 12, 3342, 178985294, 2483527716080119, 14325590005802419238355799, 50976900301828909677297289506452525838, 155682086691137998248942804080553139214788341933547854

Offset

0,2

Comments

The number of isomorphism classes of closed binary operations on sets of order <= n. See formulas by Christian G. Bower in A001329 Number of nonisomorphic groupoids with n elements.

Links

Table of n, a(n) for n=0..8.

Formula

a(n) = SUM[i=0..n] A001329(i). a(n) = SUM[i=0..n] (A079173(i)+A027851(i)). a(n) = SUM[i=0..n] (A079177(i)+A079180(i)). a(n) = SUM[i=0..n] (A079183(i)+A001425(i)). a(n) = SUM[i=0..n] (A079187(i)+A079190(i)). a(n) = SUM[i=0..n] (A079193(i)+A079196(i)+A079199(i)+A001426(i)).

Example

a(5) = 1 + 1 + 10 + 3330 + 178981952 + 2483527537094825 = 2483527716080119 is prime.

Crossrefs

Cf. A001424, A001425, A002489, A006448, A029850, A030245-A030265, A030271, A038015-A038023.

Sequence in context: A357765 A003042 A000887 * A007155 A265092 A262032

Adjacent sequences: A118539 A118540 A118541 * A118543 A118544 A118545

Keyword

nonn

Author

Jonathan Vos Post, May 06 2006

Status

approved