A058142 - OEIS

%I #15 Feb 15 2022 13:57:39

%S 1,1,1,1,3,1,2,9,6,2,1,26,30,16,5,1,98,142,111,54,15,1,455,718,713,

%T 482,215,53,3,4018,4277,4637,3919,2414,996,222,2,101910,36124,32937,

%U 31308,24047,13758,5294,1078,1,10054303,708355,290278,260758,229411,164216,88178,31867,5994

%N Triangle read by rows: number of commutative monoids of order n with k idempotents.

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

%e Triangle begins:

%e   1;

%e   1,  1;

%e   1,  3,   1;

%e   2,  9,   6,   2;

%e   1, 26,  30,  16, 5;

%e   1, 98, 142, 111, 54, 15;

%e   ...

%Y Row sums give A058131.

%Y Main diagonal: A006966.

%Y Columns 1..2: A000688, A058143.

%Y Cf. A058116, A058137, A058150, A058159, A058160.

%K nonn,tabl,hard

%O 1,5

%A _Christian G. Bower_, Nov 14 2000

%E a(30)-a(55) from _Andrew Howroyd_, Feb 15 2022