A030250 Number of nonisomorphic groupoids with no idempotents.

1, 0, 3, 978, 56630832, 813802235250650, 4797611106478930201025520, 17327898558894838031017212608777367670, 53493753018329066207577438898229132113128344235601408, 187718696426064213397098486627523446172013701247783260377097623530914986

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..25

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=1, #v, prod(j=1, #v, my(g=gcd(v[i], v[j])); C(v[i]*v[j]/g, v)^g)) * prod(i=1, #v, 1 - 1/C(v[i], 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 A038018.

Cf. A001329, A391481 (labeled version).

Sequence in context: A324443 A151585 A286525 * A145231 A318480 A358269

Adjacent sequences: A030247 A030248 A030249 * A030251 A030252 A030253

Keyword

nonn

Author

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

Status

approved