A144091 T(n,k) is the number of partial bijections (or subpermutations) of an n-element set of height k (height(alpha) = |Im(alpha)|) and with exactly 2 fixed points.

1, 3, 0, 6, 12, 6, 10, 60, 90, 20, 15, 180, 630, 660, 135, 21, 420, 2730, 6720, 5565, 924, 28, 840, 8820, 39760, 76020, 51912, 7420, 36, 1512, 23436, 168840, 585900, 917784, 533988, 66744

Offset: 2

Author

Abdullahi Umar, Sep 11 2008

Keywords

• nonn
• tabl

Examples

			T(4,2) = 6 because there are exactly 6 partial bijections (on a 4-element set) with exactly 2 fixed points and of height 2, namely: the 6 partial identities on 2-element subsets of the 4-element set.
		

Links

• A. Laradji and A. Umar, Combinatorial results for the symmetric inverse semigroup, Semigroup Forum 75, (2007), 221-236.

Crossrefs

Row sums are A144087.

Programs

PARI

T(n,k) = (n!/2!*(n-k)!)*sum(m=0,k-2,((-1)^m/m!)*binomial(n-2-m,k-2-m))
for (n=2, 10, for (k=2, n, print1(T(n,k), ", "))) \\ Michel Marcus, Apr 27 2016

Formula

T(n,k) = (n!/2!(n-k)!)sum(m=0,k-2,(-1^m/m!)C(n-2-m,k-2-m)).