|
Search: id:A102356
|
|
|
| A102356 |
|
Problem 65 in Knuth's Art of Computer Programming, vol. 4, section 7.2.1.5 asks which integer partition of n produces the most set partitions. The n-th term of this sequence is the number of set partitions produced by that integer partition. |
|
+0
4
|
|
| 1, 1, 1, 3, 6, 15, 60, 210, 840, 3780, 12600, 69300, 415800, 2702700, 12612600, 94594500, 756756000, 4288284000, 38594556000, 244432188000, 1833241410000
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
LINKS
|
D. E. Knuth, The Art of Computer Programming, vol. 4
|
|
EXAMPLE
|
a(4)=6 because there are 6 set partitions of type {2,1,1}; all other integer partitions of 4 produce fewer set partitions.
|
|
MATHEMATICA
|
sp[l_] := (Total[l])!/(Apply[Times, Map[ #! &, l]]*Apply[Times, Map[Count[l, # ]! &, Range[Max[l]]]]) a[n_] := Max[Map[sp, Partitions[n]]]
|
|
CROSSREFS
|
Sequence in context: A005655 A051169 A051610 this_sequence A102936 A009192 A013273
Adjacent sequences: A102353 A102354 A102355 this_sequence A102357 A102358 A102359
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Dan Drake (drake(AT)math.umn.edu), Feb 21 2005
|
|
|
Search completed in 0.002 seconds
|
