

A144091


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


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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
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OFFSET

2,2


LINKS



FORMULA

T(n,k) = (n!/2!(nk)!)sum(m=0,k2,(1^m/m!)C(n2m,k2m)).


EXAMPLE

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


PROG

(PARI) T(n, k) = (n!/2!*(nk)!)*sum(m=0, k2, ((1)^m/m!)*binomial(n2m, k2m))
for (n=2, 10, for (k=2, n, print1(T(n, k), ", "))) \\ Michel Marcus, Apr 27 2016


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



