A068740 - OEIS

%I #27 Dec 27 2017 02:12:29

%S 1,1,3,833712928048000000

%N Result after dividing (n^n)! as many times as possible by n!.

%C For prime n, it is also the number of generalized knockout tournament seedings with n players in one match and n rounds (see formula below). - _Alexander Karpov_, Dec 14 2017

%C Next term is too large to include.

%C From _Robert G. Wilson v_, Dec 14 2017: (Start)

%C a(4) = 4125147631...      (370 digits)...3291015625,

%C a(5) = 3483655217...     (7923 digits)...3819109376,

%C a(6) = 2196422024...   (164237 digits)...0161431552,

%C a(7) = 4948281440...  (4005981 digits)...0000000000,

%C a(8) = 4242413765...(102886160 digits)...4619140625,

%C (End)

%H Robert G. Wilson v, <a href="/A068740/b068740.txt">Table of n, a(n) for n = 0..4</a>

%H Alexander Karpov, <a href="https://wp.hse.ru/data/2017/12/12/1160180715/WP7_2017_03_________.pdf">Generalized knockout tournaments</a>, National Research University Higher School of Economics. WP7/2017/03.

%F a(n) = A068741(n)/A068742(n).

%F For p prime, a(p) = (p^p)!/(p!)^((p^p-1)/(p-1)).

%e a(3)=833712928048000000 since 3!=6 and (3^3)!=27!=10888869450418352160768000000 which is divisible by 6^13=13060694016 but not 6^14=78364164096.

%Y Cf. A000142, A000312, A023037, A057599, A068741, A068742.

%K nonn

%O 0,3

%A _Henry Bottomley_, Feb 26 2002