A058159 - OEIS

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A058159

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

8

1, 2, 2, 3, 18, 6, 16, 180, 144, 36, 30, 2040, 3240, 1740, 380, 360, 43170, 81000, 70740, 31680, 6390, 840, 1400112, 2589510, 2976960, 2055480, 832230, 157962, 15360, 110488616, 117733728, 144285960, 130781280, 79626120, 30004128, 5396888, 68040, 30647444544, 9223088112, 8744866704, 8997002280, 7154708400, 4005012816, 1421659512, 243179064

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

OFFSET

1,2

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) = A058160(n, k)*n.

EXAMPLE

Triangle begins:

1;

2, 2;

3, 18, 6;

16, 180, 144, 36;

30, 2040, 3240, 1740, 380;

360, 43170, 81000, 70740, 31680, 6390;

...

CROSSREFS

Row sums give A058155.

Column 1: A034382.

Main diagonal: A055512.

Cf. A058142 (isomorphism classes), A058157, A058160.

Sequence in context: A035796 A049009 A101817 * A058157 A348667 A230504

Adjacent sequences: A058156 A058157 A058158 * A058160 A058161 A058162

KEYWORD

nonn,tabl

AUTHOR

Christian G. Bower, Nov 14 2000

EXTENSIONS

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

STATUS

approved