A261125 a(n) = (2^(n-1))!*a(n-1) for n>=1, a(0) = 1.

1, 1, 2, 48, 1935360, 40493130637639680000, 10654991354747516157752604498631700563938508800000000000

Offset: 0

Author

Alexander Karpov, Aug 09 2015

Keywords

• nonn

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.

Crossrefs

Cf. A000722, A067667 (number of seedings).

Programs

Magma

[n le 1 select n else Self(n-1)*Factorial(2^(n - 1)): n in [1..7]]; // Vincenzo Librandi, Aug 10 2015

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 *)

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

Formula

a(n) = Product_{j=0..n-1} (2^j)!. - Alois P. Heinz, Feb 04 2023

Extensions

a(0)=1 prepended by Alois P. Heinz, Feb 04 2023