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A130760
Noncrossing set partition version of A102356.
3
1, 1, 1, 3, 6, 10, 30, 105, 280, 756, 2520, 6930, 18480, 60060, 180180, 675675, 2162160, 6806800, 24504480, 77597520, 232792560, 888844320, 3259095840, 10708457760, 37479602160, 133855722000
OFFSET
0,4
REFERENCES
D. E. Knuth, The Art of Computer Programming, vol. 4, section 7.2.1.5, problem 65.
LINKS
EXAMPLE
a(7) = 105 because there are 105 noncrossing set partitions of {1,2,3,4,5,6,7} of type {3,2,1,1} and all other integer partitions of 7 produce fewer noncrossing set partitions.
MATHEMATICA
<<Combinatorica`
ncsp[p_] := FactorialPower[Total[p], Length[p] - 1]/Apply[Times, Map[Factorial[Count[p, #1]] &, Range[Max[p]]]]; a[n_] := Max[Map[ncsp, Partitions[n]]];
Table[a[n], {n, 0, 20}]
CROSSREFS
Cf. A102356.
Sequence in context: A080506 A109163 A109490 * A154134 A001465 A094276
KEYWORD
nonn
AUTHOR
Dan Drake, Jul 13 2007
EXTENSIONS
Mathematica program fixed by Vaclav Kotesovec, Oct 23 2014
STATUS
approved