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

1,2

Links

Table of n, a(n) for n=1..36.

Index entries for sequences related to monoids

Formula

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

Example

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

Crossrefs

Row sums give A058153.

Column 1: A034383.

Main diagonal is A351731.

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

Sequence in context: A049009 A101817 A058159 * A348667 A230504 A265806

Adjacent sequences: A058154 A058155 A058156 * A058158 A058159 A058160

Keyword

nonn,tabl

Author

Christian G. Bower, Nov 14 2000

Extensions

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

Status

approved