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%I #17 Dec 19 2021 13:56:28
%S 1,1,1,7,192,82355,653502972,110826042515867,479732982053513924168,
%T 62082231641825701423422054735,
%U 275573192431752191557427399293883120600,47363301285150007842253190185182901101879369430257
%N Number of nonisomorphic commutative idempotent groupoids.
%H <a href="/index/Gre#groupoids">Index entries for sequences related to groupoids</a>
%F a(n) = Sum_{1*s_1+2*s_2+...=n} (fixA[s_1, s_2, ...]/(1^s_1*s_1!*2^s_2*s2!*...)) where fixA[s_1, s_2, ...] = Product_{i>=j>=1} f(i, j, s_i, s_j) where f(i, j, s_i, s_j) = {i=j, odd} (Sum_{d|i} (d*s_d))^((i*s_i^2-s_i)/2) or {i=j, even} (Sum_{d|i} (d*s_d))^((i*s_i^2-2*s_i)/2) * (Sum_{d|i/2} (d*s_d))^s_i or {i != j} (Sum_{d|lcm(i, j)} (d*s_d))^(gcd(i, j)*s_i*s_j). - Corrected by _Sean A. Irvine_, Mar 27 2020
%F a(n) is asymptotic to (n^binomial(n-1, 2))/n! = A076113(n)/A000142(n).
%Y Cf. A001329, A038017, A038021, A076113.
%K nonn
%O 0,4
%A _Christian G. Bower_, Feb 15 1998, May 15 1998 and Dec 03 2003
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