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Triangle of (multi)factorials: n-th row is (n+1)!!... {n "!"s}, (n+1)!... {n-1 "!"s}, ..., (n+1)!.
2

%I #9 May 09 2015 13:28:08

%S 2,3,6,4,8,24,5,10,15,120,6,12,18,48,720,7,14,21,28,105,5040,8,16,24,

%T 32,80,384,40320,9,18,27,36,45,162,945,362880,10,20,30,40,50,120,280,

%U 3840,3628800,11,22,33,44,55,66,231,880,10395,39916800,12,24,36,48,60,72,168

%N Triangle of (multi)factorials: n-th row is (n+1)!!... {n "!"s}, (n+1)!... {n-1 "!"s}, ..., (n+1)!.

%H Ivan Neretin, <a href="/A084980/b084980.txt">Table of n, a(n) for n = 1..4950</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Factorial.html">Factorial.</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Multifactorial.html">Multifactorial.</a>

%e Triangle begins

%e Row 1: 2! = 2

%e Row 2: 3!! = 3*1 = 3, 3! = 3*2*1 = 6

%e Row 3: 4!!! = 4*1 = 4, 4!! = 4*2 = 8, 4! = 4*3*2*1 = 24,

%e Row 4: 5!!!! = 5*1 = 5, 5!!! = 5*2 = 10, 5!! = 5*3 = 15, 5! = 5*4*3*2*1 = 120,

%e ...

%t Flatten[Table[Times @@ Range[n, 1, -i], {n, 12}, {i, n - 1, 1, -1}]] (* _Ivan Neretin_, May 09 2015 *)

%Y Cf. A000142 (n!), A006882 (n!!), A007661 (n!!!), A007662 (n!!!!).

%K nonn,tabl

%O 1,1

%A _Rick L. Shepherd_, Jul 16 2003