OFFSET
0,3
COMMENTS
The next term is too large to display.
The number of knockout tournament seedings that satisfy the delayed confrontation property.
a(n) is the number of permutations p of [2^n] such that {p(1),...,p(2^k)} = [2^k] for all k = 0..n: a(2) = 2: 1234, 1243. - Alois P. Heinz, Feb 04 2023
LINKS
Michel Marcus, Table of n, a(n) for n = 0..9
Alexander Karpov, A theory of knockout tournament seedings, Heidelberg University, AWI Discussion Paper Series, No. 600.
FORMULA
a(n) = Product_{j=0..n-1} (2^j)!. - Alois P. Heinz, Feb 04 2023
MAPLE
a:= proc(n) option remember:
`if`(n=0, 1, a(n-1)*(2^(n-1))!)
end:
seq(a(n), n=0..6); # Alois P. Heinz, Feb 04 2023
MATHEMATICA
RecurrenceTable[{a[1] == 1, a[n] == a[n-1] (2^(n - 1))!}, a, {n, 10}] (* Vincenzo Librandi, Aug 10 2015 *)
FoldList[(2^#2)!*#1&, 1, Range@6] (* Ivan N. Ianakiev, Aug 10 2015 *)
PROG
(Magma) [n le 1 select n else Self(n-1)*Factorial(2^(n - 1)): n in [1..7]]; // Vincenzo Librandi, Aug 10 2015
(PARI) first(m)=my(v=vector(m)); v[1]=1; for(i=2, m, v[i]=(2^(i-1))!*v[i-1]; ); v; \\ Anders Hellström, Aug 10 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander Karpov, Aug 09 2015
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Feb 04 2023
STATUS
approved