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.
%I A381575 #12 Mar 16 2025 10:08:38 %S A381575 1,2,7,68,4619,15621334 %N A381575 Number of disjoint-union partial algebras with zero on [n]. %C A381575 A disjoint-union partial algebra on a set S is a subset of the power set of S which is closed under union of disjoint sets. %C A381575 A disjoint-union partial algebra with zero on a set S is a disjoint-union partial algebra on S which contains the empty set. %C A381575 There are twice as many disjoint-union partial algebras on S as disjoint-union partial algebras with zero on S because the disjoint-union partial algebras without the empty set can be placed in bijection with those which have the empty set. %D A381575 Hirsch, R., & McLean, B. (2017). Disjoint-union partial algebras. Logical Methods in Computer Science, 13. %H A381575 Robin Hirsch and Brett McLean, <a href="https://arxiv.org/abs/1612.00252">Disjoint-union partial algebras</a>, arXiv:1612.00252 [math.RA], 2016-2017. %o A381575 (Python) %o A381575 def A381575(n): %o A381575 cnt=0 %o A381575 for p in range(1,2**(2**n),2): %o A381575 for a in range(1,2**n): %o A381575 if p&(1<<a): %o A381575 for b in range(a+1,2**n): %o A381575 if p&(1<<b): %o A381575 if (a&b)==0 and not p&(1<<(a|b)): %o A381575 break %o A381575 else: %o A381575 continue %o A381575 break %o A381575 else: %o A381575 cnt+=1 %o A381575 return cnt %o A381575 # _Bert Dobbelaere_, Mar 16 2025 %Y A381575 Cf. A380571, A381472 (unlabeled case). %K A381575 nonn,more %O A381575 0,2 %A A381575 _Peter J. Taylor_, Feb 28 2025