A084980 Triangle of (multi)factorials: n-th row is (n+1)!!... {n "!"s}, (n+1)!... {n-1 "!"s}, ..., (n+1)!.

2, 3, 6, 4, 8, 24, 5, 10, 15, 120, 6, 12, 18, 48, 720, 7, 14, 21, 28, 105, 5040, 8, 16, 24, 32, 80, 384, 40320, 9, 18, 27, 36, 45, 162, 945, 362880, 10, 20, 30, 40, 50, 120, 280, 3840, 3628800, 11, 22, 33, 44, 55, 66, 231, 880, 10395, 39916800, 12, 24, 36, 48, 60, 72, 168

Offset: 1

Author

Rick L. Shepherd, Jul 16 2003

Keywords

• nonn
• tabl

Examples

			Triangle begins
Row 1: 2! = 2
Row 2: 3!! = 3*1 = 3, 3! = 3*2*1 = 6
Row 3: 4!!! = 4*1 = 4, 4!! = 4*2 = 8, 4! = 4*3*2*1 = 24,
Row 4: 5!!!! = 5*1 = 5, 5!!! = 5*2 = 10, 5!! = 5*3 = 15, 5! = 5*4*3*2*1 = 120,
...
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..4950
• Eric Weisstein's World of Mathematics, Factorial.
• Eric Weisstein's World of Mathematics, Multifactorial.

Crossrefs

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

Programs

Mathematica

Flatten[Table[Times @@ Range[n, 1, -i], {n, 12}, {i, n - 1, 1, -1}]] (* Ivan Neretin, May 09 2015 *)