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A058160 Triangle read by rows: T(n,k) is the number of labeled commutative monoids of order n with k idempotents and a fixed identity.

%I A058160 #9 Feb 15 2022 16:50:28
%S A058160 1,1,1,1,6,2,4,45,36,9,6,408,648,348,76,60,7195,13500,11790,5280,1065,
%T A058160 120,200016,369930,425280,293640,118890,22566,1920,13811077,14716716,
%U A058160 18035745,16347660,9953265,3750516,674611,7560,3405271616,1024787568,971651856,999666920,794967600,445001424,157962168,27019896
%N A058160 Triangle read by rows: T(n,k) is the number of labeled commutative monoids of order n with k idempotents and a fixed identity.
%H A058160 Andrew Howroyd, <a href="/A058160/b058160.txt">Table of n, a(n) for n = 1..55</a> (rows 1..10)
%H A058160 <a href="/index/Mo#monoids">Index entries for sequences related to monoids</a>
%F A058160 T(n, k) = A058159(n, k)/n.
%e A058160 Triangle begins:
%e A058160    1;
%e A058160    1,    1;,
%e A058160    1,    6,     2;
%e A058160    4,   45,    36,     9;
%e A058160    6,  408,   648,   348,   76;
%e A058160   60, 7195, 13500, 11790, 5280, 1065;
%e A058160   ...
%Y A058160 Row sums give A058156.
%Y A058160 Column 1: A058162.
%Y A058160 Main diagonal A058164.
%Y A058160 Cf. A058142 (isomorphism classes), A058158, A058159.
%K A058160 nonn,tabl
%O A058160 1,5
%A A058160 _Christian G. Bower_, Nov 14 2000
%E A058160 Terms a(30) and beyond from _Andrew Howroyd_, Feb 15 2022