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

Author

Christian G. Bower, Nov 14 2000

Keywords

• nonn
• tabl

Examples

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

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 A058156.

Column 1: A058162.

Main diagonal A058164.

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

Formula

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

Extensions

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