A082765 Trinomial transform of the factorial numbers (A000142).

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

Offset: 0

Author

Emanuele Munarini, May 21 2003

Keywords

• easy
• nonn

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

• Robert A. Proctor, Let's Expand Rota's Twelvefold Way For Counting Partitions!, arXiv:math.CO/0606404, Jan 05, 2007
• Index entries for related partition-counting sequences

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.

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