A079200 Number of isomorphism classes of associative non-commutative closed binary operations on a set of order n, listed by class size.

0, 0, 2, 0, 2, 0, 4, 6, 2, 0, 0, 4, 5, 0, 46, 73, 2, 0, 0, 0, 4, 0, 0, 8, 0, 2, 36, 0, 43, 2, 473, 1020, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 4, 0, 36, 0, 0, 0, 0, 86, 0, 0, 38, 415, 0, 758, 32, 6682, 18426, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8

Offset: 0

Author

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

Keywords

• nonn
• tabf

Comments

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

Examples

			Triangle T(n,k) begins:
  0;
  0;
  2, 0;
  2, 0, 4, 6;
  2, 0, 0, 4, 5, 0, 46, 73;
  2, 0, 0, 0, 4, 0, 0, 8, 0, 2, 36, 0, 43, 2, 473, 1020;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..217 (rows 0..8)
• C. van den Bosch, Closed binary operations on small sets

Crossrefs

Row sums give A079199.

Cf. A027423 (row lengths), A079171, A079194, A079175, A079197, A079198, A079199, A079201, A079210.

Formula

A079194(n,k) + A079197(n,k) + T(n,k) + A079201(n,k) = A079171(n,k).

A079198(n) = Sum_{k>=1} T(n,k)*A079210(n,k).

T(n,k) = A079175(n,k) - A079201(n,k). - Andrew Howroyd, Jan 26 2022

Extensions

a(0)=0 prepended and terms a(16) and beyond from Andrew Howroyd, Jan 26 2022