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Number of non-associative non-commutative closed binary operations on a set of order n.
6

%I #11 Jan 26 2022 23:08:59

%S 0,0,6,18904,4293916368,298023193359221998,

%T 10314424798468598595515695154,

%U 256923577521058877628624940679487983651948,6277101735386680763835789098689112757675628513119817261598

%N Number of non-associative non-commutative closed binary operations on a set of order n.

%H C. van den Bosch, <a href="https://web.archive.org/web/20071014230143/http://cosmos.ucc.ie/~cjvdb1/html/binops.shtml">Closed binary operations on small sets</a>

%H <a href="/index/Gre#groupoids">Index entries for sequences related to groupoids</a>

%F a(n) + A079195(n) + A079198(n) + A023815(n) = A002489(n).

%F a(n) = Sum_{k>=1} A079194(n,k)*A079210(n,k).

%F a(n) = A002489(n) - A023813(n) - A023814(n) + A023815(n). - _Andrew Howroyd_, Jan 26 2022

%Y Cf. A002489, A023813, A023814, A023815, A079193 (isomorphism classes), A079194, A079195, A079198.

%K nonn

%O 0,3

%A Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003

%E a(0)=0 prepended and a(5)-a(8) added by _Andrew Howroyd_, Jan 26 2022