A058142 Triangle read by rows: number of commutative monoids of order n with k idempotents.

1, 1, 1, 1, 3, 1, 2, 9, 6, 2, 1, 26, 30, 16, 5, 1, 98, 142, 111, 54, 15, 1, 455, 718, 713, 482, 215, 53, 3, 4018, 4277, 4637, 3919, 2414, 996, 222, 2, 101910, 36124, 32937, 31308, 24047, 13758, 5294, 1078, 1, 10054303, 708355, 290278, 260758, 229411, 164216, 88178, 31867, 5994

Offset: 1

Author

Christian G. Bower, Nov 14 2000

Keywords

• nonn
• tabl
• hard

Examples

			Triangle begins:
  1;
  1,  1;
  1,  3,   1;
  2,  9,   6,   2;
  1, 26,  30,  16, 5;
  1, 98, 142, 111, 54, 15;
  ...
		

Links

• Index entries for sequences related to monoids

Crossrefs

Row sums give A058131.

Main diagonal: A006966.

Columns 1..2: A000688, A058143.

Cf. A058116, A058137, A058150, A058159, A058160.

Extensions

a(30)-a(55) from Andrew Howroyd, Feb 15 2022