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%I #15 Mar 01 2015 15:14:03
%S 1,4,45,1282,70177,6239016,817234189,147950506390,35370826189857,
%T 10791515504716012,4091225768720823181,1886585105032464025674,
%U 1039774852573506696192385,674970732343624159361034832
%N Trinomial transform of the factorial numbers (A000142).
%C Number of ways to use the elements of {1,..,k}, 0<=k<=2n, once each to form a sequence of n (possibly empty) lists, each of length at most 2. - Bob Proctor, Apr 18 2005
%H Robert A. Proctor, <a href="http://arxiv.org/abs/math.CO/0606404">Let's Expand Rota's Twelvefold Way For Counting Partitions!</a>, arXiv:math.CO/0606404, Jan 05, 2007
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F a(n) = Sum[ Trinomial[n, k] k!, {k, 0, 2n} ] where Trinomial[n, k] = trinomial coefficients (A027907)
%F Integral_{x=0..infinity} (x^2+x+1)^n*exp(-x) dx - _Gerald McGarvey_, Oct 14 2006
%Y a(n) = Sum[C(n, k)*A099022(k), 0<=k<=n]
%Y Replace "sequence" by "collection" in comment: A105747.
%Y Replace "lists" by "sets" in comment: A003011.
%K easy,nonn
%O 0,2
%A _Emanuele Munarini_, May 21 2003