A378232 - OEIS

%I #36 Nov 22 2024 08:56:49

%S 1,3,39,971,38140,2126890,157874467,14928602309,1741809491235,

%T 244735956424795,40624759074089024,7844197919242438656,

%U 1739438713163799330816,438224899712759850074112,124286842162679182383906816,39368769274679275493259214848,13831693583206759177535050743808

%N Cardinality of the ramified symmetric inverse monoid R(IS_n).

%C a(n) is the number of ramified set partitions (I, J), where I is a partial permutation.

%H 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 a(n) = Sum_{k=0..n}(k!*(binomial(n, k)^2)*A000110(2n - k)).

%K nonn

%O 0,2

%A _Diego Arcis_, Nov 21 2024