A058159 - OEIS

%I #10 Feb 15 2022 16:50:17

%S 1,2,2,3,18,6,16,180,144,36,30,2040,3240,1740,380,360,43170,81000,

%T 70740,31680,6390,840,1400112,2589510,2976960,2055480,832230,157962,

%U 15360,110488616,117733728,144285960,130781280,79626120,30004128,5396888,68040,30647444544,9223088112,8744866704,8997002280,7154708400,4005012816,1421659512,243179064

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

%H Andrew Howroyd, <a href="/A058159/b058159.txt">Table of n, a(n) for n = 1..55</a> (rows 1..10)

%H <a href="/index/Mo#monoids">Index entries for sequences related to monoids</a>

%F T(n, k) = A058160(n, k)*n.

%e Triangle begins:

%e     1;

%e     2,     2;

%e     3,    18,     6;

%e    16,   180,   144,    36;

%e    30,  2040,  3240,  1740,   380;

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

%e   ...

%Y Row sums give A058155.

%Y Column 1: A034382.

%Y Main diagonal: A055512.

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

%K nonn,tabl

%O 1,2

%A _Christian G. Bower_, Nov 14 2000

%E Terms a(30) and beyond from _Andrew Howroyd_, Feb 15 2022