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A068605
Number of functions from [1,2,...,n] to [1,2,...,n] such that the image contains exactly two elements.
4
2, 18, 84, 300, 930, 2646, 7112, 18360, 45990, 112530, 270204, 638820, 1490762, 3440430, 7864080, 17825520, 40107726, 89652906, 199229060, 440401500, 968883762, 2122317318, 4630511064, 10066329000, 21810380150, 47110421826, 101468601612, 217969589460, 467077692570
OFFSET
2,1
COMMENTS
The sequence is the column corresponding to k=2 in A090657. - Geoffrey Critzer, Mar 06 2009
FORMULA
a(n) = C(n, 2) * (2^n - 2).
O.g.f.: (4x^2/(1-2x)^3) - (2x^2/(1-x)^3). - Geoffrey Critzer, Mar 06 2009
E.g.f.: exp(x)*(2*exp(x) - 1)*x^2. - Stefano Spezia, May 06 2023
MATHEMATICA
Table[ Binomial[n, 2]*(2^n - 2), {n, 2, 30}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sharon Sela (sharonsela(AT)hotmail.com), Mar 29 2002
EXTENSIONS
Edited and extended by Robert G. Wilson v, Apr 17 2002
STATUS
approved