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A066655 Number of partitions of n*(n-1)/2. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Number of partitions of the number of edges of the complete graph of order n, K_n.
LINKS
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. A173519. - Reinhard Zumkeller, Feb 20 2010
Sequence in context: A211854 A200212 A149070 * A352684 A302421 A118166
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Jan 12 2002
Edited by Dean Hickerson, Jan 14 2002
STATUS
approved

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)