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 A030257 Number of nonisomorphic commutative idempotent groupoids. 4
 1, 1, 1, 7, 192, 82355, 653502972, 110826042515867, 479732982053513924168, 62082231641825701423422054735, 275573192431752191557427399293883120600, 47363301285150007842253190185182901101879369430257 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS FORMULA 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 fix A[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} (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))^(2*gcd(i, j)*s_i*s_j) a(n) asymptotic to (n^binomial(n-1, 2))/n! = A076113(n)/A000142(n) CROSSREFS Cf. A001329, A038017, A038021, A076113. Sequence in context: A198258 A200819 A024096 * A159826 A012849 A220754 Adjacent sequences:  A030254 A030255 A030256 * A030258 A030259 A030260 KEYWORD nonn AUTHOR Christian G. Bower, Feb 15 1998, May 15 1998 and Dec 03 2003 STATUS approved

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