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%I #10 Feb 17 2022 14:19:39
%S 1,1,1,1,6,4,4,45,72,35,6,528,1308,1676,604,80,19935,39700,70170,
%T 62060,16727,120,3599436,1969470,3829000,5167800,3260382,681232,2760,
%U 6085914205,281840664,294812385,481221020,482447637,228315640,38187291
%N Triangle read by rows: T(n,k) is the number of labeled monoids of order n with k idempotents and a fixed identity.
%H <a href="/index/Mo#monoids">Index entries for sequences related to monoids</a>
%F T(n,k) = A058157(n,k)/n.
%e Triangle begins:
%e 1;
%e 1, 1;
%e 1, 6, 4;
%e 4, 45, 72, 35;
%e 6, 528, 1308, 1676, 604;
%e 80, 19935, 39700, 70170, 62060, 16727;
%e ...
%Y Row sums give A058154.
%Y Column 1: A058163.
%Y Main diagonal is A351730(n-1).
%Y Cf. A058137 (isomorphism classes), A058157, A058160 (commutative), A058166.
%K nonn,tabl
%O 1,5
%A _Christian G. Bower_, Nov 14 2000
%E a(30)-a(36) from _Andrew Howroyd_, Feb 15 2022
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