A058167 Triangle read by rows: T(n,k) is the number of labeled commutative semigroups of order n with k idempotents.

1, 4, 2, 24, 30, 9, 260, 492, 312, 76, 4805, 10060, 9900, 4900, 1065, 157956, 284130, 348420, 259500, 112500, 22566, 12277440, 11892846, 14768775, 14093380, 9063600, 3592554, 674611, 3287166928, 896150920, 812261856, 854806120, 707722680, 413149464, 152565280, 27019896

Offset: 1

Author

Christian G. Bower, Nov 15 2000

Keywords

• nonn
• tabl
• hard

Examples

			Triangle begins:
     1;
     4,     2;
    24,    30,    9;
   260,   492,  312,   76;
  4805, 10060, 9900, 4900, 1065;
  ...
		

Links

• Index entries for sequences related to semigroups

Crossrefs

Row sums give A023815.

Main diagonal is A058164(n+1).

Cf. A058116 (isomorphism classes).

Extensions

a(29)-a(36) from Andrew Howroyd, Jan 27 2022