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A082765
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Trinomial transform of the factorial numbers (A000142).
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3
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1, 4, 45, 1282, 70177, 6239016, 817234189, 147950506390, 35370826189857, 10791515504716012, 4091225768720823181, 1886585105032464025674, 1039774852573506696192385, 674970732343624159361034832
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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
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LINKS
| Index entries for related partition-counting sequences
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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 (gerald.mcgarvey(AT)comcast.net), Oct 14 2006
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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.
Sequence in context: A174484 A158887 A126452 * A132873 A102894 A132552
Adjacent sequences: A082762 A082763 A082764 * A082766 A082767 A082768
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KEYWORD
| easy,nonn
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AUTHOR
| Emanuele Munarini (munarini(AT)mate.polimi.it), May 21 2003
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