cp's OEIS Frontend

A350225 Number of ordered pairs (a,g) with a in IS_n the symmetric inverse semigroup on [n] and g in symmetric group on [n] such that ag=ga.

%I A350225 #15 Dec 20 2021 18:16:15
%S A350225 1,2,10,60,480,4320,46800,554400,7459200,108864000,1745452800,
%T A350225 30017433600,558036864000,11021826816000,232330146048000,
%U A350225 5173159799808000,121812482727936000,3012672515973120000,78301030421053440000,2127572806150471680000,60438151687124090880000
%N A350225 Number of ordered pairs (a,g) with a in IS_n the symmetric inverse semigroup on [n] and g in symmetric group on [n] such that ag=ga.
%F A350225 a(n) = A000712(n)*n!
%p A350225 a:= proc(n) option remember; `if`(n=0, 1, 2*(n-1)!*
%p A350225       add(a(j)/j!*numtheory[sigma](n-j), j=0..n-1))
%p A350225     end:
%p A350225 seq(a(n), n=0..20);  # _Alois P. Heinz_, Dec 20 2021
%t A350225 nn = 16; Table[Sum[PartitionsP[k] PartitionsP[n - k], {k, 0, n}], {n, 0, nn}] Table[n!, {n, 0, nn}]
%Y A350225 Cf. A000142, A000712, A053529, A349739.
%K A350225 nonn
%O A350225 0,2
%A A350225 _Geoffrey Critzer_, Dec 20 2021