A068740 Result after dividing (n^n)! as many times as possible by n!.

1, 1, 3, 833712928048000000

Offset: 0

Author

Henry Bottomley, Feb 26 2002

Keywords

• nonn

Comments

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

Next term is too large to include.

From Robert G. Wilson v, Dec 14 2017: (Start)

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

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

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

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

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

(End)

Examples

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

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..4
• Alexander Karpov, Generalized knockout tournaments, National Research University Higher School of Economics. WP7/2017/03.

Crossrefs

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

Formula

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

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