cp's OEIS Frontend

A079200 Number of isomorphism classes of associative non-commutative closed binary operations on a set of order n, listed by class size.

%I A079200 #13 Jan 27 2022 18:20:07
%S A079200 0,0,2,0,2,0,4,6,2,0,0,4,5,0,46,73,2,0,0,0,4,0,0,8,0,2,36,0,43,2,473,
%T A079200 1020,2,0,0,0,0,4,0,0,0,0,8,0,0,4,0,36,0,0,0,0,86,0,0,38,415,0,758,32,
%U A079200 6682,18426,2,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,8
%N A079200 Number of isomorphism classes of associative non-commutative closed binary operations on a set of order n, listed by class size.
%C A079200 Number of elements per row: 1,1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!).
%H A079200 Andrew Howroyd, <a href="/A079200/b079200.txt">Table of n, a(n) for n = 0..217</a> (rows 0..8)
%H A079200 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>
%F A079200 A079194(n,k) + A079197(n,k) + T(n,k) + A079201(n,k) = A079171(n,k).
%F A079200 A079198(n) = Sum_{k>=1} T(n,k)*A079210(n,k).
%F A079200 T(n,k) = A079175(n,k) - A079201(n,k). - _Andrew Howroyd_, Jan 26 2022
%e A079200 Triangle T(n,k) begins:
%e A079200   0;
%e A079200   0;
%e A079200   2, 0;
%e A079200   2, 0, 4, 6;
%e A079200   2, 0, 0, 4, 5, 0, 46, 73;
%e A079200   2, 0, 0, 0, 4, 0, 0, 8, 0, 2, 36, 0, 43, 2, 473, 1020;
%e A079200   ...
%Y A079200 Row sums give A079199.
%Y A079200 Cf. A027423 (row lengths), A079171, A079194, A079175, A079197, A079198, A079199, A079201, A079210.
%K A079200 nonn,tabf
%O A079200 0,3
%A A079200 Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003
%E A079200 a(0)=0 prepended and terms a(16) and beyond from _Andrew Howroyd_, Jan 26 2022