A079194 Number of isomorphism classes of non-associative non-commutative closed binary operations on a set of order n, listed by class size.

0, 0, 2, 2, 0, 8, 66, 3115, 0, 1, 14, 18, 270, 467, 48260, 178888824

Offset

0,3

Comments

Elements per row: 1,1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!)

Links

Table of n, a(n) for n=0..15.

C. van den Bosch, Closed binary operations on small sets

Index entries for sequences related to groupoids

Formula

T(n,k) + A079197(n,k) + A079200(n,k) + A079201(n,k) = A079171(n,k).

A079192(n,k) = Sum_{k>=1} T(n,k)*A079210(n,k).

Example

Triangle T(n,k) begins:
  0;
  0;
  2, 2;
  0, 8, 66, 3115;
  0, 1, 14, 18, 270, 467, 48260, 178888824;
  ...

Crossrefs

Row sums give A079193.

Cf. A027423 (row lengths), A079171, A079192, A079197, A079200, A079201, A079210.

Sequence in context: A009803 A009615 A184011 * A179198 A372390 A117739

Adjacent sequences: A079191 A079192 A079193 * A079195 A079196 A079197

Keyword

nonn,tabf,hard,more

Author

Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003

Extensions

a(0)=0 prepended by Andrew Howroyd, Jan 26 2022

Status

approved