OFFSET
0,3
COMMENTS
Note that if n=p^k for p prime then a(n) is coprime to n (i.e., a(n) is not divisible by p).
a(n) is also the number of labelings for the simple graph K_n X K_n, the graph Cartesian product of the complete graph with itself. - Geoffrey Critzer, Oct 16 2016
a(n) is also the number of knockout tournament seedings with 2 rounds and n participants in each match. - Alexander Karpov, Dec 15 2017
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..27
Alexander Karpov, Generalized knockout tournaments, National Research University Higher School of Economics. WP7/2017/03.
FORMULA
a(n) ~ exp(n - 1/12) * n^((n-1)*(2*n-1)/2) / (2*Pi)^(n/2). - Vaclav Kotesovec, Nov 23 2018
EXAMPLE
a(2)=3 since the possibilities are {{0,1},{2,3}}; {{0,2},{1,3}}; and {{0,3},{1,2}}.
MAPLE
a:= n-> (n^2)!/(n!)^(n+1):
seq(a(n), n=0..10); # Alois P. Heinz, Apr 29 2020
MATHEMATICA
Table[a[z_] := z^n/n!; (n^2)! Coefficient[Series[a[a[z]], {z, 0, n^2}], z^(n^2)], {n, 1, 10}] (* Geoffrey Critzer, Oct 16 2016 *)
PROG
(PARI) a(n) = (n^2)!/(n!)^(n+1); \\ Altug Alkan, Dec 17 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Oct 06 2000
STATUS
approved