A058160 - OEIS

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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.

7

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

(list; table; graph; refs; listen; history; text; internal format)

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