The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A058157

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A058157

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

#15 by Michael De Vlieger at Thu Feb 17 14:19:33 EST 2022

STATUS

reviewed

approved

#14 by Michel Marcus at Thu Feb 17 11:53:15 EST 2022

STATUS

proposed

reviewed

#13 by Andrew Howroyd at Thu Feb 17 11:47:18 EST 2022

STATUS

editing

proposed

#12 by Andrew Howroyd at Thu Feb 17 11:19:25 EST 2022

CROSSREFS

Cf. A058137 (isomorphism classes), A058166, A058158, A058159 (commutative), A058166.

#11 by Andrew Howroyd at Thu Feb 17 11:14:24 EST 2022

CROSSREFS

Main diagonal is A351731.

Cf. A058137 (isomorphism classes), A058166, A058158, A058159 (commutative).

#10 by Andrew Howroyd at Tue Feb 15 14:22:04 EST 2022

EXTENSIONS

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

#9 by Andrew Howroyd at Tue Feb 15 14:21:39 EST 2022

NAME

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

DATA

1, 2, 2, 3, 18, 12, 16, 180, 288, 140, 30, 2640, 6540, 8380, 3020, 480, 119610, 238200, 421020, 372360, 100362, 840, 25196052, 13786290, 26803000, 36174600, 22822674, 4768624, 22080, 48687313640, 2254725312, 2358499080, 3849768160, 3859581096, 1826525120, 305498328

FORMULA

aT(n,k) = A058158(n,k)*n.

EXAMPLE

Triangle begins:

CROSSREFS

Cf. A058158, A058159.

KEYWORD

nonn,tabl,more

EXTENSIONS

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

STATUS

approved

editing

#8 by Alois P. Heinz at Fri Jul 16 16:42:03 EDT 2021

STATUS

editing

approved

#7 by Alois P. Heinz at Fri Jul 16 16:42:01 EDT 2021

FORMULA

a(n,k) = A058158(n,k)*n.

CROSSREFS

a(n, k)=A058158(n, k)*n. Row sums give A058153. Column 1: A034383.

Row sums give A058153.

Column 1: A034383.

Cf. A058158.

#6 by Alois P. Heinz at Thu Jul 15 19:00:09 EDT 2021

EXAMPLE

1; 2,2; 3,18,12; 16,180,288,140; 30,2640,6540,8380,3020; ...

1;

2, 2;

3, 18, 12;

16, 180, 288, 140;

30, 2640, 6540, 8380, 3020;

...

STATUS

approved

editing