A175882 Number of groupoids of order n with no identity element.

1, 0, 12, 19440, 4293918720, 298022460937500000, 10314424627908807366593740800, 256923577502496762167593902921782457650400, 6277101735385253516143083463326608130132905949327651766272, 196627050475552807506414708879663572595247698231546775823411085055396409324160

Offset: 0

Author

Matt Westwood, Dec 05 2010

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..20
• ProofWiki, Count of Binary Operations Without Identity

Crossrefs

Cf. A002489, A090602.

Programs

PARI

a(n) = n^(n^2) - n^(((n-1)^2)+1) \\ Andrew Howroyd, Jan 23 2022

Formula

a(n) = n^(n^2) - n^(((n-1)^2)+1) = A002489(n) - A090602(n).

Extensions

a(0)=1 prepended and terms a(7) and beyond from Andrew Howroyd, Jan 23 2022