A130760 Noncrossing set partition version of A102356.

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

Vaclav Kotesovec, Table of n, a(n) for n = 0..75

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

Adjacent sequences: A130757 A130758 A130759 * A130761 A130762 A130763

Keyword

nonn

Author

Dan Drake, Jul 13 2007

Extensions

Mathematica program fixed by Vaclav Kotesovec, Oct 23 2014

Status

approved