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%I #13 Dec 19 2021 13:43:55
%S 1,2,15,944,725500,9319882896,2537598028922726,
%T 17768840869582166129408,3754397843576564028373337684409,
%U 27480138271604938576005130925123233245100
%N Number of n-element self-converse groupoids with an identity.
%C Also partial self-converse groupoids with n-1 elements or self-converse groupoids with an absorbant (zero) element with n elements.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Groupoid.html">Groupoid</a>
%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, ...] = prod {i>=j>=1} f(i, j, s_i, s_j) where f(i, j, s_i, s_j) = {i=j, odd} (1 + sum {d|i*2} (d*s_d)) ^ ((i*s_i^2-s_i)/2) * (1 + sum {d|i} (d*s_d))^s_i or {i=j == 0 mod 4} (1 + sum {d|i} (d*s_d))^(i*s_i^2) or {i=j == 2 mod 4} (1 + sum {d|i})^(i*s_i^2-s_i) * (1 + sum {d|i/2} (d*s_d))^(2*s_i) or {i != j} (1 + sum {d|lcm(i, j, 2)} (d*s_d))^(2*gcd(i, j)*s_i*s_j/(s_i*s_j*lcm(2*i*j)))
%K nonn
%O 1,2
%A _Christian G. Bower_, Dec 05 2003
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