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A126063
Triangle read by rows: see A128196 for definition.
2
1, 1, 2, 3, 6, 4, 15, 30, 20, 8, 105, 210, 140, 56, 16, 945, 1890, 1260, 504, 144, 32, 10395, 20790, 13860, 5544, 1584, 352, 64, 135135, 270270, 180180, 72072, 20592, 4576, 832, 128, 2027025, 4054050, 2702700, 1081080, 308880, 68640, 12480, 1920, 256
OFFSET
0,3
LINKS
FORMULA
Let H be the diagonal matrix diag(1,2,4,8,...) and
let G be the matrix (n!! defined as A001147(n), -1!! = 1):
(-1)!!/(-1)!!
1!!/(-1)!! 1!!/1!!
3!!/(-1)!! 3!!/1!! 3!!/3!!
5!!/(-1)!! 5!!/1!! 5!!/3!! 5!!/5!!
...
Then T = G*H. [Gottfried Helms]
T(n,k) = 2^k*(2n - 1)!!/(2k - 1)!!. - Ivan Neretin, May 13 2015
EXAMPLE
Triangle begins:
1
1, 2
3, 6, 4
15, 30, 20, 8
105, 210, 140, 56, 16
945, 1890, 1260, 504, 144, 32
10395, 20790, 13860, 5544, 1584, 352, 64
135135, 270270, 180180, 72072, 20592, 4576, 832, 128
MAPLE
A126063 := (n, k) -> 2^k*doublefactorial(2*n-1)/ doublefactorial(2*k-1); seq(print(seq(A126063(n, k), k=0..n)), n=0..7); # Peter Luschny, Dec 20 2012
MATHEMATICA
Flatten[Table[2^k (2n - 1)!!/(2k - 1)!!, {n, 0, 8}, {k, 0, n}]] (* Ivan Neretin, May 11 2015 *)
CROSSREFS
First column is A001147, second column is A097801.
The diagonal is A000079, the subdiagonal is A014480.
Sequence in context: A318846 A231263 A231451 * A214352 A248090 A229774
KEYWORD
nonn,tabl,easy
AUTHOR
N. J. A. Sloane, Feb 28 2007
STATUS
approved