A138379 Number of embedded coalitions in an n-person game where the position of the individual player is important.

1, 6, 60, 888, 18120, 485280, 16445520, 685722240, 34411184640, 2041544736000, 141106965753600, 11223409849344000, 1016591564596608000, 103921686070339737600, 11896153817325313536000

Offset: 1

Author

David Yeung (wkyeung(AT)hkbu.edu.hk), May 08 2008

Keywords

• nonn

Comments

See A005493 for references and links.

Examples

			a(1) = 1 * SUM(i=0 to 0)combination(1,i) = 1,
a(2) = 2 * SUM(i=0 to 1)combination(2,i) = 6,
a(3) = 3![combination(3,2) * a(1)/1! + combination(3,2) + combination(3,1) + combination(3,0)] = 60,
a(4) = 4![combination(4,3) * {a(2)/2! + a(1)/1!} + combination(4,2) * a(1)/1! + combination(4,3) + combination(4,2) + combination(4,1) + combination(4,0)] = 888,
a(5) = 5![combination(5,4) * {a(3)/3! + a(2)/2! + a(1)/1!} + combination(5,3) * {a(2)/2! + a(1)/1!} + combination(5,2) * a(1)/1! + combination(5,4) + combination(5,3) + combination(5,2) + combination(5,1) + combination(5,0)] = 18120.
		

Formula

a(1) = 1 * SUM(i=0 to 0)combination(1,i) = 1, a(2) = 2 * SUM(i=0 to 1)combination(2,i) = 6, a(n) = n![SUM(i=2 to n-1) combination(n,i) * {SUM(j=1 to i-1) * a(j)/j! } + SUM(i=0 to n-1) combination(n,i)], for n > 2.