A030260 Number of nonisomorphic commutative groupoids with no idempotents.

1, 0, 1, 38, 13872, 83360520, 10203847031340, 31023254154131753920, 2765562268014305034000397632, 8332535835277886736134596954072281240, 960864308045670310058158724983067048253497223280, 4736330128450010934162593250279157339899194091274313266810212

Offset

0,4

Links

Andrew Howroyd, Table of n, a(n) for n = 0..36

Index entries for sequences related to groupoids

Prog

(PARI)
permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
C(d, r)={sum(i=1, #r, my(t=r[i]); if(d%t==0, t))}
E(v) = {prod(i=2, #v, prod(j=1, i-1, my(g=gcd(v[i], v[j])); C(v[i]*v[j]/g, v)^g)) * prod(i=1, #v, my(t=v[i]); C(t, v)^((t-1)\2)*(C(t, v)-1)*if(t%2, 1, C(t/2, v)))}
a(n) = {my(s=0); forpart(p=n, s += permcount(p)*E(p)); s/n!} \\ Andrew Howroyd, Dec 10 2025

Crossrefs

Column k=0 of A038021.

Cf. A001329, A001425, A391483 (labeled version).

Sequence in context: A355589 A145120 A183581 * A145122 A134182 A110017

Adjacent sequences: A030257 A030258 A030259 * A030261 A030262 A030263

Keyword

nonn

Author

Christian G. Bower, Feb 15 1998 and May 15 1998

Status

approved