

A082765


Trinomial transform of the factorial numbers (A000142).


3



1, 4, 45, 1282, 70177, 6239016, 817234189, 147950506390, 35370826189857, 10791515504716012, 4091225768720823181, 1886585105032464025674, 1039774852573506696192385, 674970732343624159361034832
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OFFSET

0,2


COMMENTS

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


LINKS



FORMULA

a(n) = Sum[ Trinomial[n, k] k!, {k, 0, 2n} ] where Trinomial[n, k] = trinomial coefficients (A027907)
Integral_{x=0..infinity} (x^2+x+1)^n*exp(x) dx  Gerald McGarvey, Oct 14 2006


CROSSREFS

a(n) = Sum[C(n, k)*A099022(k), 0<=k<=n]
Replace "sequence" by "collection" in comment: A105747.
Replace "lists" by "sets" in comment: A003011.


KEYWORD

easy,nonn


AUTHOR



STATUS

approved



