A174335 Upper bound in enumerating what majority decisions are possible with possible abstaining.

0, 16, 256, 2592, 24576, 240000, 2488320, 27659520, 330301440, 4232632320, 58060800000, 850068172800, 13243436236800, 218892235161600, 3827475696844800, 70614415872000000, 1371195958099968000

Offset: 0

Author

Jonathan Vos Post, Mar 16 2010

Keywords

• easy
• nonn

Comments

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

Examples

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

References

• 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.

Links

• P. Erdos and L. Moser, On the representation of directed graphs as unions of orderings, Magyar Tud. Akad. Mat. Kutats Int. Kvzl., 9:125-132, 1964.
• Paul Larson, Nick Matteo, Saharon Shelah, What majority decisions are possible with possible abstaining, arXiv:1003.2756 [math.CO], 2010.
• S. Shelah, What majority decisions are possible, Discrete Mathematics, 309(8): 2349-2364, 2009.

Crossrefs

Cf. A000142, A000578, A091363.

Programs

Mathematica

Table[16n^3 n!,{n,0,20}] (* Harvey P. Dale, Feb 25 2016 *)

PARI

a(n) = 16*n^3*n! \\ Michel Marcus, Jun 25 2015

Formula

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

a(n) = 16*A091363(n). - Michel Marcus, Jun 25 2015