OFFSET
0,3
COMMENTS
a(n) is also the number of knockout tournament seedings with 2^n teams. - Alexander Karpov, Aug 09 2015
From Zhujun Zhang, Jun 17 2019: (Start)
a(n) is also the number of heap-ordered binomial trees of order n (i.e., binomial heaps with 2^n nodes), see the Mark R. Brown reference.
a(n) is also the largest odd divisor of (2^n)!. (End)
LINKS
Jianing Song, Table of n, a(n) for n = 0..8
Mark R. Brown, Implementation and analysis of binomial queue algorithms, SIAM Journal on Computing, 1978, 7(3):298-319.
Alexander Karpov, A theory of knockout tournament seedings, Heidelberg University, AWI Discussion Paper Series, No. 600.
Zhujun Zhang, A Note on Counting Binomial Heaps, ResearchGate, June 2019.
FORMULA
From Alexander Karpov, Aug 09 2015: (Start)
a(n) = (2^n)!/2^(2^n-1).
a(n) = (2^n-1)!!*a(n-1).
a(n) = binomial(2^n-1, 2^(n-1)-1)*(a(n-1))^2 = A069954(n-1) * (a(n-1))^2.
(End)
a(n) = A049606(2^n). - Zhujun Zhang, Jun 16 2019
a(n) = Product_{odd k < 2^n} k^(n - floor(log_2(k))). - Harry Richman, May 18 2023
MATHEMATICA
Table[(2^n)! / 2^(2^n - 1), {n, 6}] (* Vincenzo Librandi, Aug 10 2015 *)
PROG
(Magma) [Factorial(2^n)/2^(2^n-1): n in [1..6]]; // Vincenzo Librandi, Aug 10 2015
(PARI) a(n) = (2^n)!/2^(2^n-1) \\ Jianing Song, Jul 15 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Feb 04 2002
EXTENSIONS
a(0) prepended by Jianing Song, Jul 15 2021
STATUS
approved