A058159 Triangle read by rows: T(n,k) is the number of labeled commutative monoids of order n with k idempotents.

1, 2, 2, 3, 18, 6, 16, 180, 144, 36, 30, 2040, 3240, 1740, 380, 360, 43170, 81000, 70740, 31680, 6390, 840, 1400112, 2589510, 2976960, 2055480, 832230, 157962, 15360, 110488616, 117733728, 144285960, 130781280, 79626120, 30004128, 5396888, 68040, 30647444544, 9223088112, 8744866704, 8997002280, 7154708400, 4005012816, 1421659512, 243179064

Offset: 1

Author

Christian G. Bower, Nov 14 2000

Keywords

• nonn
• tabl

Examples

			Triangle begins:
    1;
    2,     2;
    3,    18,     6;
   16,   180,   144,    36;
   30,  2040,  3240,  1740,   380;
  360, 43170, 81000, 70740, 31680, 6390;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..55 (rows 1..10)
• Index entries for sequences related to monoids

Crossrefs

Row sums give A058155.

Column 1: A034382.

Main diagonal: A055512.

Cf. A058142 (isomorphism classes), A058157, A058160.

Formula

T(n, k) = A058160(n, k)*n.

Extensions

Terms a(30) and beyond from Andrew Howroyd, Feb 15 2022