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A058167 Triangle read by rows: T(n,k) is the number of labeled commutative semigroups of order n with k idempotents.

%I A058167 #9 Jan 27 2022 18:19:44
%S A058167 1,4,2,24,30,9,260,492,312,76,4805,10060,9900,4900,1065,157956,284130,
%T A058167 348420,259500,112500,22566,12277440,11892846,14768775,14093380,
%U A058167 9063600,3592554,674611,3287166928,896150920,812261856,854806120,707722680,413149464,152565280,27019896
%N A058167 Triangle read by rows: T(n,k) is the number of labeled commutative semigroups of order n with k idempotents.
%H A058167 <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>
%e A058167 Triangle begins:
%e A058167      1;
%e A058167      4,     2;
%e A058167     24,    30,    9;
%e A058167    260,   492,  312,   76;
%e A058167   4805, 10060, 9900, 4900, 1065;
%e A058167   ...
%Y A058167 Row sums give A023815.
%Y A058167 Main diagonal is A058164(n+1).
%Y A058167 Cf. A058116 (isomorphism classes).
%K A058167 nonn,tabl,hard
%O A058167 1,2
%A A058167 _Christian G. Bower_, Nov 15 2000
%E A058167 a(29)-a(36) from _Andrew Howroyd_, Jan 27 2022