A066655 - OEIS

%I #28 May 17 2018 06:36:45

%S 1,1,3,11,42,176,792,3718,17977,89134,451276,2323520,12132164,

%T 64112359,342325709,1844349560,10015581680,54770336324,301384802048,

%U 1667727404093,9275102575355,51820051838712,290726957916112,1637293969337171,9253082936723602

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

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

%H G. C. Greubel, <a href="/A066655/b066655.txt">Table of n, a(n) for n = 1..1000</a>

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

%F a(n) ~ exp(Pi*sqrt(n*(n-1)/3))/(2*sqrt(3)*n*(n - 1)). - _Ilya Gutkovskiy_, Jan 13 2017

%F a(n) ~ exp(Pi*(n - 1/2) / sqrt(3)) / (2*sqrt(3)*n^2). - _Vaclav Kotesovec_, May 17 2018

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

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

%o (MuPAD) combinat::partitions::count(binomial(n+2,n)) $n=-1..40 // _Zerinvary Lajos_, Apr 16 2007

%o (PARI) a(n) = numbpart(n*(n-1)/2); \\ _Michel Marcus_, Dec 18 2017

%Y Cf. A000041, A000217, A007294, A104383.

%Y Cf. A173519. - _Reinhard Zumkeller_, Feb 20 2010

%K nonn

%O 1,3

%A _Roberto E. Martinez II_, Jan 10 2002

%E More terms from _Vladeta Jovovic_, Jan 12 2002

%E Edited by _Dean Hickerson_, Jan 14 2002