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Number of functions from [1,2,...,n] to [1,2,...,n] such that the image contains exactly two elements.
4

%I #25 May 08 2023 09:35:07

%S 2,18,84,300,930,2646,7112,18360,45990,112530,270204,638820,1490762,

%T 3440430,7864080,17825520,40107726,89652906,199229060,440401500,

%U 968883762,2122317318,4630511064,10066329000,21810380150,47110421826,101468601612,217969589460,467077692570

%N Number of functions from [1,2,...,n] to [1,2,...,n] such that the image contains exactly two elements.

%C The sequence is the column corresponding to k=2 in A090657. - _Geoffrey Critzer_, Mar 06 2009

%H Stefano Spezia, <a href="/A068605/b068605.txt">Table of n, a(n) for n = 2..3200</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (9,-33,63,-66,36,-8).

%F a(n) = C(n, 2) * (2^n - 2).

%F O.g.f.: (4x^2/(1-2x)^3) - (2x^2/(1-x)^3). - _Geoffrey Critzer_, Mar 06 2009

%F E.g.f.: exp(x)*(2*exp(x) - 1)*x^2. - _Stefano Spezia_, May 06 2023

%t Table[ Binomial[n, 2]*(2^n - 2), {n, 2, 30}]

%Y Cf. A000918, A090657, A161680.

%K nonn,easy

%O 2,1

%A Sharon Sela (sharonsela(AT)hotmail.com), Mar 29 2002

%E Edited and extended by _Robert G. Wilson v_, Apr 17 2002