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

1,2

Comments

See A005493 for references and links.

Links

Table of n, a(n) for n=1..15.

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.

Example

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.

Crossrefs

Sequence in context: A099708 A177191 A010040 * A064815 A331120 A368505

Adjacent sequences: A138376 A138377 A138378 * A138380 A138381 A138382

Keyword

nonn

Author

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

Status

approved