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

1,2

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).

Links

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

Formula

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

Example

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]

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 *)

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.

Sequence in context: A133492 A045663 A128092 * A032503 A050838 A374512

Adjacent sequences: A167566 A167567 A167568 * A167570 A167571 A167572

Keyword

easy,nonn,tabl

Author

Johannes W. Meijer, Nov 10 2009

Status

approved