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

1, 3, 39, 971, 38140, 2126890, 157874467, 14928602309, 1741809491235, 244735956424795, 40624759074089024, 7844197919242438656, 1739438713163799330816, 438224899712759850074112, 124286842162679182383906816, 39368769274679275493259214848, 13831693583206759177535050743808

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..16.

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

Formula

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

Crossrefs

Sequence in context: A258923 A326271 A276964 * A367596 A353739 A274573

Adjacent sequences: A378229 A378230 A378231 * A378233 A378234 A378235

Keyword

nonn

Author

Diego Arcis, Nov 21 2024

Status

approved