cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A023815 Number of binary operations on an n-set that are commutative and associative; labeled commutative semigroups.

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%I A023815 #23 Feb 16 2025 08:32:34
%S A023815 1,1,6,63,1140,30730,1185072,66363206,7150843144,3829117403448
%N A023815 Number of binary operations on an n-set that are commutative and associative; labeled commutative semigroups.
%H A023815 Eric Postpischil <a href="http://groups.google.com/groups?&amp;hl=en&amp;lr=&amp;ie=UTF-8&amp;selm=11802%40shlump.nac.dec.com&amp;rnum=2">Posting to sci.math newsgroup, May 21 1990</a>
%H A023815 Amit Sehgal, Sunil Kumar, Sarita, Yashpal, <a href="https://doi.org/10.1088/1742-6596/1000/1/012063">Commutative Associative Binary Operations on a Set with Five Elements</a>, J. Phys.: Conf. Ser. (2018) 1000 012063
%H A023815 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semigroup.html">Semigroup.</a>
%H A023815 <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>
%F A023815 a(n) + A079192(n) + A079195(n) + A079198(n) = A002489(n).
%F A023815 a(n) = Sum_{k>=1} A079201(n,k)*A079210(n,k). - _Andrew Howroyd_, Jan 26 2022
%Y A023815 Row sums of A058167.
%Y A023815 Cf. A001423, A001426 (isomorphism classes), A023813 (commutative only), A023814 (associative only), A027851.
%Y A023815 Cf. A002489, A079192, A079195, A079198, A079201, A079210.
%K A023815 nonn,hard,more
%O A023815 0,3
%A A023815 Lyle Ramshaw (ramshaw(AT)pa.dec.com)
%E A023815 a(8) from _Andrew Howroyd_, Jan 26 2022
%E A023815 a(9) from _Andrew Howroyd_, Feb 14 2022