A066655 Number of partitions of n*(n-1)/2.

1, 1, 3, 11, 42, 176, 792, 3718, 17977, 89134, 451276, 2323520, 12132164, 64112359, 342325709, 1844349560, 10015581680, 54770336324, 301384802048, 1667727404093, 9275102575355, 51820051838712, 290726957916112, 1637293969337171, 9253082936723602

Offset: 1

Author

Roberto E. Martinez II, Jan 10 2002

Keywords

• nonn

Comments

Number of partitions of the number of edges of the complete graph of order n, K_n.

Examples

			a(4) = p(6) = 11.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000041, A000217, A007294, A104383.

Cf. A173519. - Reinhard Zumkeller, Feb 20 2010

Programs

Mathematica

Table[PartitionsP[n(n-1)/2], {n, 1, 30}]

MuPAD

combinat::partitions::count(binomial(n+2,n)) $n=-1..40 // Zerinvary Lajos, Apr 16 2007

PARI

a(n) = numbpart(n*(n-1)/2); \\ Michel Marcus, Dec 18 2017

Formula

a(n) = p(n*(n-1)/2) = A000041(n*(n-1)/2).

a(n) ~ exp(Pi*sqrt(n*(n-1)/3))/(2*sqrt(3)*n*(n - 1)). - Ilya Gutkovskiy, Jan 13 2017

a(n) ~ exp(Pi*(n - 1/2) / sqrt(3)) / (2*sqrt(3)*n^2). - Vaclav Kotesovec, May 17 2018

Extensions

More terms from Vladeta Jovovic, Jan 12 2002

Edited by Dean Hickerson, Jan 14 2002