A058157 Triangle read by rows: T(n,k) is the number of labeled monoids of order n with k idempotents.

1, 2, 2, 3, 18, 12, 16, 180, 288, 140, 30, 2640, 6540, 8380, 3020, 480, 119610, 238200, 421020, 372360, 100362, 840, 25196052, 13786290, 26803000, 36174600, 22822674, 4768624, 22080, 48687313640, 2254725312, 2358499080, 3849768160, 3859581096, 1826525120, 305498328

Offset: 1

Author

Christian G. Bower, Nov 14 2000

Keywords

• nonn
• tabl

Examples

			Triangle begins:
   1;
   2,    2;
   3,   18,   12;
  16,  180,  288,  140;
  30, 2640, 6540, 8380, 3020;
  ...
		

Links

• Index entries for sequences related to monoids

Crossrefs

Row sums give A058153.

Column 1: A034383.

Main diagonal is A351731.

Cf. A058137 (isomorphism classes), A058158, A058159 (commutative), A058166.

Formula

T(n,k) = A058158(n,k)*n.

Extensions

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