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.

A322654 Number of binary operations on an n-set that satisfy (ab)c = (ac)b for all a,b,c.

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%I A322654 #16 Feb 11 2019 19:50:44
%S A322654 1,1,10,573,136528,115511945,365045461056
%N A322654 Number of binary operations on an n-set that satisfy (ab)c = (ac)b for all a,b,c.
%C A322654 Equivalently, these are operations for which the functions induced by right multiplication commute with one another. The operations of subtraction, division, and exponentiation satisfy this identity on appropriate domains.
%H A322654 J. Benaloh and M. de Mare, <a href="https://doi.org/10.1007/3-540-48285-7_24">One-Way Accumulators: A Decentralized Alternative to Digital Signatures</a>, in: Tor Helleseth, Advances in Cryptology — EUROCRYPT '93, Springer-Verlag Berlin Heidelberg, 1994, 274-285 (<a href="https://www.microsoft.com/en-us/research/wp-content/uploads/1993/01/owa.pdf">Link to PDF</a>).
%F A322654 a(n) = Sum_{k=1..n} k!*Stirling2(n,k)*c(n,k), where c(n,k) is the number of sets of k distinct functions from {1..n} to itself that are mutually commutative.
%Y A322654 Cf. A019538, A254570.
%K A322654 nonn,more
%O A322654 0,3
%A A322654 _David Radcliffe_, Dec 21 2018