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%I #20 Dec 19 2021 13:49:27
%S 1,1,4,138,60160,453292525,72471180989664,298545867396801815077,
%T 37263960166680610905649057368,
%U 161614516495439236943507628117344255307,27480138271604938271870114918720067827110789528890
%N Number of self-converse 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, ...] = prod {i>=j>=1} f(i, j, s_i, s_j) where f(i, j, s_i, s_j) = {i=j, odd} (sum {d|i*2} (d*s_d))^((i*s_i^2-s_i)/2) * (sum {d|i} (d*s_d))^s_i or {i=j == 0 mod 4} (sum {d|i} (d*s_d))^(i*s_i^2) or {i=j == 2 mod 4} (sum {d|i} (d*s_d))^(i*s_i^2-s_i) * (sum {d|i/2} (d*s_d))^(2*s_i) or {i != j} (sum {d|lcm(i, j, 2)} (d*s_d))^(2*i*j*s_i*s_j/lcm(2*i*j)).
%Y a(n) = 2*A001424(n) - A001329(n). Cf. A001425.
%K nonn
%O 0,3
%A _Christian G. Bower_, Jan 15 1998, Jun 15 1998, Dec 05 2003
%E Formula corrected by _Sean A. Irvine_ and _Christian G. Bower_, Jul 13 2012
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