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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.

%I A058159 #10 Feb 15 2022 16:50:17
%S A058159 1,2,2,3,18,6,16,180,144,36,30,2040,3240,1740,380,360,43170,81000,
%T A058159 70740,31680,6390,840,1400112,2589510,2976960,2055480,832230,157962,
%U A058159 15360,110488616,117733728,144285960,130781280,79626120,30004128,5396888,68040,30647444544,9223088112,8744866704,8997002280,7154708400,4005012816,1421659512,243179064
%N A058159 Triangle read by rows: T(n,k) is the number of labeled commutative monoids of order n with k idempotents.
%H A058159 Andrew Howroyd, <a href="/A058159/b058159.txt">Table of n, a(n) for n = 1..55</a> (rows 1..10)
%H A058159 <a href="/index/Mo#monoids">Index entries for sequences related to monoids</a>
%F A058159 T(n, k) = A058160(n, k)*n.
%e A058159 Triangle begins:
%e A058159     1;
%e A058159     2,     2;
%e A058159     3,    18,     6;
%e A058159    16,   180,   144,    36;
%e A058159    30,  2040,  3240,  1740,   380;
%e A058159   360, 43170, 81000, 70740, 31680, 6390;
%e A058159   ...
%Y A058159 Row sums give A058155.
%Y A058159 Column 1: A034382.
%Y A058159 Main diagonal: A055512.
%Y A058159 Cf. A058142 (isomorphism classes), A058157, A058160.
%K A058159 nonn,tabl
%O A058159 1,2
%A A058159 _Christian G. Bower_, Nov 14 2000
%E A058159 Terms a(30) and beyond from _Andrew Howroyd_, Feb 15 2022