A082765 Trinomial transform of the factorial numbers (A000142).

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

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

Table of n, a(n) for n=0..13.

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

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.

Sequence in context: A174484 A158887 A126452 * A132873 A244753 A335014

Adjacent sequences: A082762 A082763 A082764 * A082766 A082767 A082768

Keyword

easy,nonn

Author

Emanuele Munarini, May 21 2003

Status

approved