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

1,3

Comments

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

Links

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

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000041, A000217, A007294, A104383.

Cf. A173519. - Reinhard Zumkeller, Feb 20 2010

Sequence in context: A211854 A200212 A149070 * A352684 A302421 A118166

Adjacent sequences: A066652 A066653 A066654 * A066656 A066657 A066658

Keyword

nonn

Author

Roberto E. Martinez II, Jan 10 2002

Extensions

More terms from Vladeta Jovovic, Jan 12 2002

Edited by Dean Hickerson, Jan 14 2002

Status

approved