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 A029850 Number of self-converse groupoids. 3
 1, 1, 4, 138, 60160, 453292525, 72471180989664, 298545867396801815077, 37263960166680610905649057368, 161614516495439236943507628117344255307, 27480138271604938271870114918720067827110789528890 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA 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)). CROSSREFS a(n) = 2*A001424(n) - A001329(n). Cf. A001425. Sequence in context: A155207 A201388 A089666 * A221675 A340838 A291450 Adjacent sequences: A029847 A029848 A029849 * A029851 A029852 A029853 KEYWORD nonn AUTHOR Christian G. Bower, Jan 15 1998, Jun 15 1998, Dec 05 2003 EXTENSIONS Formula corrected by Sean A. Irvine and Christian G. Bower, Jul 13 2012 STATUS approved

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Last modified March 27 05:46 EDT 2023. Contains 361554 sequences. (Running on oeis4.)