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A068740 Result after dividing (n^n)! as many times as possible by n!. 3
1, 1, 3, 833712928048000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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)

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.

FORMULA

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

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

EXAMPLE

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

CROSSREFS

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

Sequence in context: A216148 A058453 A058471 * A058473 A115527 A050920

Adjacent sequences:  A068737 A068738 A068739 * A068741 A068742 A068743

KEYWORD

nonn

AUTHOR

Henry Bottomley, Feb 26 2002

STATUS

approved

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Last modified February 21 00:34 EST 2020. Contains 332086 sequences. (Running on oeis4.)