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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 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
2,2
LINKS
A. Laradji and A. Umar, Combinatorial results for the symmetric inverse semigroup, Semigroup Forum 75, (2007), 221-236.
FORMULA
T(n,k) = (n!/2!(n-k)!)sum(m=0,k-2,(-1^m/m!)C(n-2-m,k-2-m)).
EXAMPLE
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.
PROG
(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
CROSSREFS
Row sums are A144087.
Sequence in context: A141434 A077911 A057381 * A019145 A059684 A270509
KEYWORD
nonn,tabl
AUTHOR
Abdullahi Umar, Sep 11 2008
STATUS
approved

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Last modified July 17 12:34 EDT 2024. Contains 374377 sequences. (Running on oeis4.)