A058160 Triangle read by rows: T(n,k) is the number of labeled commutative monoids of order n with k idempotents and a fixed identity.

1, 1, 1, 1, 6, 2, 4, 45, 36, 9, 6, 408, 648, 348, 76, 60, 7195, 13500, 11790, 5280, 1065, 120, 200016, 369930, 425280, 293640, 118890, 22566, 1920, 13811077, 14716716, 18035745, 16347660, 9953265, 3750516, 674611, 7560, 3405271616, 1024787568, 971651856, 999666920, 794967600, 445001424, 157962168, 27019896

Offset

1,5

Links

Andrew Howroyd, Table of n, a(n) for n = 1..55 (rows 1..10)

Index entries for sequences related to monoids

Formula

T(n, k) = A058159(n, k)/n.

Example

Triangle begins:
   1;
   1,    1;,
   1,    6,     2;
   4,   45,    36,     9;
   6,  408,   648,   348,   76;
  60, 7195, 13500, 11790, 5280, 1065;
  ...

Crossrefs

Row sums give A058156.

Column 1: A058162.

Main diagonal A058164.

Cf. A058142 (isomorphism classes), A058158, A058159.

Sequence in context: A027599 A351297 A248272 * A033939 A021020 A215578

Adjacent sequences: A058157 A058158 A058159 * A058161 A058162 A058163

Keyword

nonn,tabl

Author

Christian G. Bower, Nov 14 2000

Extensions

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

Status

approved