A058158 Triangle read by rows: T(n,k) is the number of labeled monoids of order n with k idempotents and a fixed identity.

1, 1, 1, 1, 6, 4, 4, 45, 72, 35, 6, 528, 1308, 1676, 604, 80, 19935, 39700, 70170, 62060, 16727, 120, 3599436, 1969470, 3829000, 5167800, 3260382, 681232, 2760, 6085914205, 281840664, 294812385, 481221020, 482447637, 228315640, 38187291

Offset

1,5

Links

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

Index entries for sequences related to monoids

Formula

T(n,k) = A058157(n,k)/n.

Example

Triangle begins:
   1;
   1,     1;
   1,     6,     4;
   4,    45,    72,    35;
   6,   528,  1308,  1676,   604;
  80, 19935, 39700, 70170, 62060, 16727;
  ...

Crossrefs

Row sums give A058154.

Column 1: A058163.

Main diagonal is A351730(n-1).

Cf. A058137 (isomorphism classes), A058157, A058160 (commutative), A058166.

Sequence in context: A330934 A019174 A019166 * A249185 A021159 A106332

Adjacent sequences: A058155 A058156 A058157 * A058159 A058160 A058161

Keyword

nonn,tabl

Author

Christian G. Bower, Nov 14 2000

Extensions

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

Status

approved