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%I #15 Dec 19 2021 13:47:56
%S 1,1,3,138,700688,794734575200,307047114275109035760,
%T 61899500454067972015948863454485,
%U 9279375475116928325576506574232168143663715776
%N Number of nonisomorphic idempotent groupoids.
%H <a href="/index/Gre#groupoids">Index entries for sequences related to groupoids</a>
%F For a list n(1), n(2), n(3), ..., let fixF[n] = prod{i, j >= 1}(sum{d|[ i, j ]}(d*n(d))^((i, j)*n(i)*n(j)-(i=j)n(i))).
%F a(n) = sum {1*s_1+2*s_2+...=n} (fix A[s_1, s_2, ...]/(1^s_1*s_1!*2^s_2*s2!*...)) where fixA[s_1, s_2, ...] = prod {i>=j>=1} f(i, j, s_i, s_j) where f(i, j, s_i, s_j) = {i=j} (sum {d|i} (d*s_d))^(i*s_i^2-s_i) or {i != j} (sum {d|lcm(i, j)} (d*s_d))^(2*gcd(i, j)*s_i*s_j)
%F a(n) asymptotic to (n^(n^2-n))/n! = A090588(n)/A000142(n)
%Y Cf. A001329, A038015, A038018, A090588.
%K nonn
%O 0,3
%A _Christian G. Bower_, Feb 15 1998, May 15 1998 and Dec 03 2003
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