A167569 The lower left triangle of the ED2 array A167560.

1, 2, 4, 6, 16, 32, 24, 80, 192, 384, 120, 480, 1344, 3072, 6144, 720, 3360, 10752, 27648, 61440, 122880, 5040, 26880, 96768, 276480, 675840, 1474560, 2949120, 40320, 241920, 967680, 3041280, 8110080, 19169280, 41287680, 82575360

Offset: 1

Author

Johannes W. Meijer, Nov 10 2009

Keywords

• easy
• nonn
• tabl

Comments

We discovered that the numbers that appear in the lower left triangle of the ED2 array A167560 (m <= n) behave in a regular way, see the formula below. This rather simple regularity doesn't show up in the upper right triangle of the ED2 array (m > n).

Examples

			The first few triangle rows are:
[1]
[2, 4]
[6, 16, 32]
[24, 80, 192, 384]
[120, 480, 1344, 3072, 6144]
[720, 3360, 10752, 27648, 61440, 122880]
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows

Crossrefs

A167560 is the ED2 array.

A047053, 2*A034177 and A167570 are the first three right hand triangle columns.

A000142, 4*A001715, 32*A001725, 384* A049388 and 6144* A049398 are the first five left hand triangle columns.

A167571 equals the row sums.

Programs

Maple

a := proc(n, m): 4^(m-1)*(m-1)!*(n+m-1)!/(2*m-1)! end: seq(seq(a(n, m), m=1..n), n=1..8); # Johannes W. Meijer, revised Nov 23 2012

Mathematica

Flatten[Table[4^(m - 1)*(m - 1)!*(n + m - 1)!/(2*m - 1)!, {n, 1, 50}, {m, n}]] (* G. C. Greubel, Jun 16 2016 *)

Formula

a(n,m) = 4^(m-1)*(m-1)!*(n+m-1)!/(2*m-1)!.