A058158 Triangle read by rows: T(n,k) is the number of labeled monoids of order n with k idempotents and a fixed identity.

1, 1, 1, 1, 6, 4, 4, 45, 72, 35, 6, 528, 1308, 1676, 604, 80, 19935, 39700, 70170, 62060, 16727, 120, 3599436, 1969470, 3829000, 5167800, 3260382, 681232, 2760, 6085914205, 281840664, 294812385, 481221020, 482447637, 228315640, 38187291

Offset: 1

Author

Christian G. Bower, Nov 14 2000

Keywords

• nonn
• tabl

Examples

			Triangle begins:
   1;
   1,     1;
   1,     6,     4;
   4,    45,    72,    35;
   6,   528,  1308,  1676,   604;
  80, 19935, 39700, 70170, 62060, 16727;
  ...
		

Links

• Index entries for sequences related to monoids

Crossrefs

Row sums give A058154.

Column 1: A058163.

Main diagonal is A351730(n-1).

Cf. A058137 (isomorphism classes), A058157, A058160 (commutative), A058166.

Formula

T(n,k) = A058157(n,k)/n.

Extensions

a(30)-a(36) from Andrew Howroyd, Feb 15 2022