A351731 -id:A351731 - cp's OEIS frontend

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

Christian G. Bower, Nov 14 2000

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

Index entries for sequences related to monoids

Row sums give A058153.
Column 1: A034383.
Main diagonal is A351731.
Cf. A058137 (isomorphism classes), A058158, A058159 (commutative), A058166.

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

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

A351730 Number of labeled idempotent semigroups of order n.

Original entry on oeis.org

1, 1, 4, 35, 604, 16727, 681232, 38187291, 2810370122, 261999605819

Offset: 0

Andrew Howroyd, Feb 17 2022

a(n) is also the number of labeled idempotent monoids of order n+1 with a fixed identity.

Main diagonal of A058166 and A058158.

Cf. A023814, A058112 (isomorphism classes), A351731.

cp's OEIS Frontend

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

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A351730 Number of labeled idempotent semigroups of order n.

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