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[C(n, k)*(n+k)!/2^k, 0<=k<=n]

14 = |{ ({1},{2}), ({2},{1}), ({1},{2,3}), ({2,3},{1}), ({2},{1,3}), ({1,3},{2}), ({3},{1,2}), ({1,2},{3}), ({1,2},{3,4}), ({3,4},{1,2}), ({1,3},{2,4}), ({2,4},{1,3}), ({1,4},{2,3}), ({2,3},{1,4}) }|

f[n_] := Sum[ Binomial[n, k](n + k)!/2^k, {k, 0, n}]; Table[ f[n], {n, 0, 14}]

a(n) = n!*A001515(n).

A003011(n) = Sum[C(n, k)*a(k), 0<=k<=n].

Replace "sets" by "lists": A099022.

Sequence in context: A136550 A068369 A034405 this_sequence A118086 A048163 A093548

Adjacent sequences: A105746 A105747 A105748 this_sequence A105750 A105751 A105752

nonn,easy

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

More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 23 2005