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

%I A261125 #40 Feb 04 2023 10:56:02
%S A261125 1,1,2,48,1935360,40493130637639680000,
%T A261125 10654991354747516157752604498631700563938508800000000000
%N A261125 a(n) = (2^(n-1))!*a(n-1) for n>=1, a(0) = 1.
%C A261125 The next term is too large to display.
%C A261125 The number of knockout tournament seedings that satisfy the delayed confrontation property.
%C A261125 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
%H A261125 Michel Marcus, <a href="/A261125/b261125.txt">Table of n, a(n) for n = 0..9</a>
%H A261125 Alexander Karpov, <a href="http://www.uni-heidelberg.de/md/awi/forschung/dp600.pdf">A theory of knockout tournament seedings</a>, Heidelberg University, AWI Discussion Paper Series, No. 600.
%F A261125 a(n) = Product_{j=0..n-1} (2^j)!. - _Alois P. Heinz_, Feb 04 2023
%p A261125 a:= proc(n) option remember:
%p A261125       `if`(n=0, 1, a(n-1)*(2^(n-1))!)
%p A261125     end:
%p A261125 seq(a(n), n=0..6);  # _Alois P. Heinz_, Feb 04 2023
%t A261125 RecurrenceTable[{a[1] == 1, a[n] == a[n-1] (2^(n - 1))!}, a, {n, 10}] (* _Vincenzo Librandi_, Aug 10 2015 *)
%t A261125 FoldList[(2^#2)!*#1&,1,Range@6] (* _Ivan N. Ianakiev_, Aug 10 2015 *)
%o A261125 (Magma) [n le 1 select n else Self(n-1)*Factorial(2^(n - 1)): n in [1..7]]; // _Vincenzo Librandi_, Aug 10 2015
%o A261125 (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
%Y A261125 Cf. A000722, A067667 (number of seedings).
%K A261125 nonn
%O A261125 0,3
%A A261125 _Alexander Karpov_, Aug 09 2015
%E A261125 a(0)=1 prepended by _Alois P. Heinz_, Feb 04 2023