A030257 - OEIS

A030257

Number of nonisomorphic commutative idempotent groupoids.

1, 1, 1, 7, 192, 82355, 653502972, 110826042515867, 479732982053513924168, 62082231641825701423422054735, 275573192431752191557427399293883120600, 47363301285150007842253190185182901101879369430257

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..11.

Index entries for sequences related to groupoids

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

Cf. A001329, A038017, A038021, A076113.

Sequence in context: A232146 A264353 A024096 * A159826 A012849 A308610

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