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 A378232 #43 Aug 13 2025 23:07:49
%S A378232 1,3,39,971,38140,2126890,157874467,14928602309,1741809491235,
%T A378232 244735956424795,40624759074089022,7844197919242437824,
%U A378232 1739438713163799078369,438224899712759948799899,124286842162679198452748231,39368769274679276781570308187,13831693583206758886731727544652
%N A378232 Cardinality of the ramified symmetric inverse monoid R(IS_n).
%C A378232 a(n) is the number of ramified set partitions (I, J), where I is a partial permutation.
%H A378232 Francesca Aicardi, Diego Arcis, and Jesús Juyumaya, <a href="https://www.doi.org/10.17323/1609-4514-2024-24-3-321-355">Ramified inverse and planar monoids</a>, Mosc Math J, 24(3):321-355, 9 2024.
%F A378232 a(n) = Sum_{k=0..n}(k!*(binomial(n, k)^2)*A000110(2n - k)).
%p A378232 seq(add(k!*(binomial(n, k)^2)*combinat:-bell(2*n - k),k=0..n),n=0..16); # _Georg Fischer_, Jun 16 2025
%Y A378232 Cf. A000110.
%K A378232 nonn
%O A378232 0,2
%A A378232 _Diego Arcis_, Nov 21 2024
%E A378232 a(10)-a(16) corrected by _Georg Fischer_, Jun 16 2025