0,2

R. A. Proctor, Let's Expand Rota's Twelvefold Way for Counting Partitions! arXiv math.CO.0606404.

Index entries for related partition-counting sequences

Sum[(k+i)!/i!/(k-i)!, 0<=i<=k<=n]

Sequence satisfies the recurrence a(n+3)=(4n+11)a(n+2)-(4n+9)a(n+1)-a(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 26 2006

23 = |{ {(),()}, {(),(1)}, {(),(1,2)}, {(),(2,1)}, {(1),(2)}, {(1),(2,3)}, {(1),(3,2)},..,{(1,4),(2,3)}, {(1,4),(3,2)}, {(4,1),(2,3)}, {(4,1),(3,2)} }|

Sum[(k+i)!/i!/(k-i)!, {k, 0, n}, {i, 0, k}]

First differences: A001517.

Replace "collection" by "sequence": A082765.

Replace "lists" by "sets": A105748.

Adjacent sequences: A105744 A105745 A105746 this_sequence A105748 A105749 A105750

Sequence in context: A108953 A099869 A056785 this_sequence A099692 A123637 A130890

nonn,easy

Robert A. Proctor (www.math.unc.edu/Faculty/rap/), Apr 18 2005