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A082765 Trinomial transform of the factorial numbers (A000142). 3
1, 4, 45, 1282, 70177, 6239016, 817234189, 147950506390, 35370826189857, 10791515504716012, 4091225768720823181, 1886585105032464025674, 1039774852573506696192385, 674970732343624159361034832 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 15:07 EST 2022. Contains 350607 sequences. (Running on oeis4.)