A179268 - OEIS

%I #11 Sep 08 2022 08:45:54

%S 1,24,181440,3487131648000,646300418472124416000000,

%T 3099944389915843478899995401256960000000,

%U 844835922269816056767016893501799134566045599137792000000000

%N Product of numbers between and including n and n^2.

%C a(n) = Product_{k=n..n^2} k;

%C a(n) = A088020(n)/A000142(n-1).

%H Vincenzo Librandi, <a href="/A179268/b179268.txt">Table of n, a(n) for n = 1..23</a>

%F a(n) = (n^2)! / (n-1)!.

%e a(2) = 2*3*4 = 24;

%e a(3) = 3*4*5*6*7*8*9 = 181440.

%t Table[Times@@Range[n,n^2],{n,10}] (* _Harvey P. Dale_, Sep 16 2020 *)

%o (Magma) [Factorial(n^2) / Factorial(n-1): n in [1..10]]; // _Vincenzo Librandi_, May 31 2011

%Y Cf. A126804, A027441.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Jul 06 2010

%E Definition clarified by _Harvey P. Dale_, Sep 16 2020