A378232 Cardinality of the ramified symmetric inverse monoid R(IS_n).

1, 3, 39, 971, 38140, 2126890, 157874467, 14928602309, 1741809491235, 244735956424795, 40624759074089022, 7844197919242437824, 1739438713163799078369, 438224899712759948799899, 124286842162679198452748231, 39368769274679276781570308187, 13831693583206758886731727544652

Offset: 0

Author

Diego Arcis, Nov 21 2024

Keywords

• nonn

Comments

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

Links

• Francesca Aicardi, Diego Arcis, and Jesús Juyumaya, Ramified inverse and planar monoids, Mosc Math J, 24(3):321-355, 9 2024.

Crossrefs

Cf. A000110.

Programs

Maple

seq(add(k!*(binomial(n, k)^2)*combinat:-bell(2*n - k),k=0..n),n=0..16); # Georg Fischer, Jun 16 2025

Formula

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

Extensions

a(10)-a(16) corrected by Georg Fischer, Jun 16 2025