A174335 - OEIS

%I #11 Feb 25 2016 16:53:12

%S 0,16,256,2592,24576,240000,2488320,27659520,330301440,4232632320,

%T 58060800000,850068172800,13243436236800,218892235161600,

%U 3827475696844800,70614415872000000,1371195958099968000

%N Upper bound in enumerating what majority decisions are possible with possible abstaining.

%C a(n) from last equations, Larson, p.22.

%D J. A. N. d. Condorcet. Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix. L'imprimerie royale, Paris, 1785.

%H P. Erdos and L. Moser, <a href="https://www.renyi.hu/~p_erdos/1964-22.pdf">On the representation of directed graphs as unions of orderings</a>, Magyar Tud. Akad. Mat. Kutats Int. Kvzl., 9:125-132, 1964.

%H Paul Larson, Nick Matteo, Saharon Shelah, <a href="http://arxiv.org/abs/1003.2756">What majority decisions are possible with possible abstaining</a>, arXiv:1003.2756 [math.CO], 2010.

%H S. Shelah, <a href="http://dx.doi.org/10.1016/j.disc.2008.05.010">What majority decisions are possible</a>, Discrete Mathematics, 309(8): 2349-2364, 2009.

%F a(n) = 16*(n^3)*(n!) = 16*A000578(n)*A000142(n).

%F a(n) = 16*A091363(n). - _Michel Marcus_, Jun 25 2015

%e a(4) = 16*(4^3)*(4!) = 24576.

%t Table[16n^3 n!,{n,0,20}] (* _Harvey P. Dale_, Feb 25 2016 *)

%o (PARI) a(n) = 16*n^3*n! \\ _Michel Marcus_, Jun 25 2015

%Y Cf. A000142, A000578, A091363.

%K easy,nonn

%O 0,2

%A _Jonathan Vos Post_, Mar 16 2010