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 A038017 Number of n-element commutative groupoids with an identity ("pointed" groupoids). 2
 1, 2, 15, 720, 409600, 3920030472, 775775333825891, 3837862827737186253664, 558740081065710564284870598075, 2755731923933734753149997221152548428020, 520996314135332606285488148844494695722050333912483 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also number of commutative partial groupoids with n-1 elements or commutative groupoids with an absorbant (zero) element with n elements. LINKS Table of n, a(n) for n=1..11. Eric Postpischil Posting to sci.math newsgroup, May 21 1990 Eric Weisstein's World of Mathematics, Groupoid. Index entries for sequences related to groupoids FORMULA a(n+1) = 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} (d*s_d))^((i*s_i^2+s_i)/2) or {i=j, even} (1 + sum {d|i} (d*s_d))^(i*s_i^2/2) * (1 + sum {d|i/2} (d*s_d))^s_i or {i != j} (1 + sum {d|lcm(i, j)} (d*s_d))^(2*gcd(i, j)*s_i*s_j) a(n) asymptotic to (n^binomial(n, 2)+1)/n! = A090599(n)/A000142(n) = A076113(n)/A000142(n-1) CROSSREFS Cf. A001329, A030257. Sequence in context: A013064 A013095 A208051 * A012993 A216331 A179432 Adjacent sequences: A038014 A038015 A038016 * A038018 A038019 A038020 KEYWORD nonn AUTHOR Christian G. Bower, May 15 1998; revised Dec 05 2003 STATUS approved

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Last modified September 29 06:43 EDT 2023. Contains 365757 sequences. (Running on oeis4.)