|
|
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} (fixA[s_1, s_2, ...]/(1^s_1*s_1!*2^s_2*s2!*...)) where fixA[s_1, s_2, ...] = Product_{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))^(gcd(i, j)*s_i*s_j). - Corrected by Sean A. Irvine, Mar 27 2020
a(n) is asymptotic to (n^binomial(n-1, 2))/n! = A076113(n)/A000142(n).
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|