A126063 - OEIS

%I #28 Nov 16 2022 04:36:25

%S 1,1,2,3,6,4,15,30,20,8,105,210,140,56,16,945,1890,1260,504,144,32,

%T 10395,20790,13860,5544,1584,352,64,135135,270270,180180,72072,20592,

%U 4576,832,128,2027025,4054050,2702700,1081080,308880,68640,12480,1920,256

%N Triangle read by rows: see A128196 for definition.

%H Ivan Neretin, <a href="/A126063/b126063.txt">Rows n = 0..100, flattened</a>

%H P. Luschny, <a href="http://www.luschny.de/math/seq/variations.html">Variants of Variations</a>.

%F Let H be the diagonal matrix diag(1,2,4,8,...) and

%F let G be the matrix (n!! defined as A001147(n), -1!! = 1):

%F (-1)!!/(-1)!!

%F 1!!/(-1)!! 1!!/1!!

%F 3!!/(-1)!! 3!!/1!! 3!!/3!!

%F 5!!/(-1)!! 5!!/1!! 5!!/3!! 5!!/5!!

%F ...

%F Then T = G*H. [Gottfried Helms]

%F T(n,k) = 2^k*(2n - 1)!!/(2k - 1)!!. - _Ivan Neretin_, May 13 2015

%e Triangle begins:

%e        1

%e        1,       2

%e        3,       6,       4

%e       15,      30,      20,       8

%e      105,     210,     140,      56,     16

%e      945,    1890,    1260,     504,    144,    32

%e    10395,   20790,   13860,    5544,   1584,   352,    64

%e   135135,  270270,  180180,   72072,  20592,  4576,   832,  128

%p 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

%t Flatten[Table[2^k (2n - 1)!!/(2k - 1)!!, {n, 0, 8}, {k, 0, n}]] (* _Ivan Neretin_, May 11 2015 *)

%Y First column is A001147, second column is A097801.

%Y The diagonal is A000079, the subdiagonal is A014480.

%K nonn,tabl,easy

%O 0,3

%A _N. J. A. Sloane_, Feb 28 2007