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A167569
The lower left triangle of the ED2 array A167560.
6
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).
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
KEYWORD
easy,nonn,tabl
AUTHOR
Johannes W. Meijer, Nov 10 2009
STATUS
approved