A125031 Total number of highest scorers in all 2^(n(n-1)/2) tournaments with n players.

1, 2, 12, 104, 1560, 53184, 3422384, 430790144, 111823251840, 56741417927680, 57729973360342272, 118195918779085344768, 479770203506298422135808, 3914602958361039682677710848, 63809077054456699374663196416000, 2076906726499655025703507210668998656

Offset: 1

Author

Martin Fuller, Nov 16 2006

Keywords

• nonn

Comments

All highest scorers are also king chickens, A123553.

Examples

			With 4 players there are 32 tournaments with 1 highest scorer, 24 tournaments with 2 highest scorers and 8 tournaments with 3 highest scorers. Therefore a(4)=32*1+24*2+8*3=104.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..20
• Index entries for sequences related to tournaments

Crossrefs

Cf. A006125, A013976, A123553, A125032, A123903.

Programs

PARI

\\ Requires Winners from A013976.
a(n)={my(M=Winners(n)); sum(i=1, matsize(M)[1], pollead(M[i, 1])*M[i, 2])} \\ Andrew Howroyd, Feb 29 2020

Extensions

a(5)-a(10) also computed by Gordon Royle, Nov 16 2006

Terms a(12) and beyond from Andrew Howroyd, Feb 28 2020