OFFSET
0,3
LINKS
Ivan Neretin, Rows n = 0..100, flattened
P. Luschny, Variants of Variations.
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
KEYWORD
AUTHOR
N. J. A. Sloane, Feb 28 2007
STATUS
approved