1,2

Also number of commutative partial groupoids with n-1 elements or commutative groupoids with an absorbant (zero) element with n elements.

Eric Postpischil Posting to sci.math newsgroup, May 21 1990

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for sequences related to groupoids

a(n+1) = 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} (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)

Cf. A001329, A030257.

Sequence in context: A071627 A013064 A013095 this_sequence A012993 A007542 A090604

Adjacent sequences: A038014 A038015 A038016 this_sequence A038018 A038019 A038020

nonn

Christian G. Bower (bowerc(AT)usa.net), May 15 1998; revised Dec 05 2003