cp's OEIS Frontend

A079201 Number of isomorphism classes of associative commutative closed binary operations on a set of order n, listed by class size.

%I A079201 #15 Jan 27 2022 18:19:58
%S A079201 1,1,0,3,0,0,3,9,0,0,0,3,0,0,16,39,0,0,0,0,2,0,0,0,0,0,15,0,4,0,103,
%T A079201 201,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,12,0,0,0,0,6,0,0,4,91,0,55,0,715,
%U A079201 1258,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12
%N A079201 Number of isomorphism classes of associative commutative closed binary operations on a set of order n, listed by class size.
%C A079201 Number of elements per row: 1,1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!).
%H A079201 Andrew Howroyd, <a href="/A079201/b079201.txt">Table of n, a(n) for n = 0..217</a> (rows 0..8)
%H A079201 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 A079201 <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>
%F A079201 A079194(n,k) + A079197(n,k) + A079200(n,k) + T(n,k) = A079171(n,k).
%F A079201 T(n, A027423(n)) = A058105(n).
%F A079201 A023815(n) = Sum_{k>=1} T(n,k)*A079210(n,k).
%e A079201 Triangle T(n,k) begins:
%e A079201   1;
%e A079201   1;
%e A079201   0, 3;
%e A079201   0, 0, 3, 9;
%e A079201   0, 0, 0, 3, 0, 0, 16, 39;
%e A079201   0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 15, 0, 4, 0, 103, 201;
%Y A079201 Row sums are A001426.
%Y A079201 Cf. A023815, A027423 (row lengths), A079171, A079194, A079197, A079200, A058105.
%K A079201 nonn,tabf
%O A079201 0,4
%A A079201 Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003
%E A079201 a(0)=1 prepended and terms a(16) and beyond from _Andrew Howroyd_, Jan 26 2022