A030247 Number of nonisomorphic idempotent groupoids.

1, 1, 3, 138, 700688, 794734575200, 307047114275109035760, 61899500454067972015948863454485, 9279375475116928325576506574232168143663715776

Offset: 0

Author

Christian G. Bower, Feb 15 1998, May 15 1998 and Dec 03 2003

Keywords

• nonn

Links

• Index entries for sequences related to groupoids

Crossrefs

Cf. A001329, A038015, A038018, A090588.

Formula

For a list n(1), n(2), n(3), ..., let fixF[n] = prod{i, j >= 1}(sum{d|[ i, j ]}(d*n(d))^((i, j)*n(i)*n(j)-(i=j)n(i))).

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 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} (sum {d|i} (d*s_d))^(i*s_i^2-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^(n^2-n))/n! = A090588(n)/A000142(n)