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A126063 Triangle read by rows: see A128196 for definition.

%I A126063 #28 Nov 16 2022 04:36:25
%S A126063 1,1,2,3,6,4,15,30,20,8,105,210,140,56,16,945,1890,1260,504,144,32,
%T A126063 10395,20790,13860,5544,1584,352,64,135135,270270,180180,72072,20592,
%U A126063 4576,832,128,2027025,4054050,2702700,1081080,308880,68640,12480,1920,256
%N A126063 Triangle read by rows: see A128196 for definition.
%H A126063 Ivan Neretin, <a href="/A126063/b126063.txt">Rows n = 0..100, flattened</a>
%H A126063 P. Luschny, <a href="http://www.luschny.de/math/seq/variations.html">Variants of Variations</a>.
%F A126063 Let H be the diagonal matrix diag(1,2,4,8,...) and
%F A126063 let G be the matrix (n!! defined as A001147(n), -1!! = 1):
%F A126063 (-1)!!/(-1)!!
%F A126063 1!!/(-1)!! 1!!/1!!
%F A126063 3!!/(-1)!! 3!!/1!! 3!!/3!!
%F A126063 5!!/(-1)!! 5!!/1!! 5!!/3!! 5!!/5!!
%F A126063 ...
%F A126063 Then T = G*H. [Gottfried Helms]
%F A126063 T(n,k) = 2^k*(2n - 1)!!/(2k - 1)!!. - _Ivan Neretin_, May 13 2015
%e A126063 Triangle begins:
%e A126063        1
%e A126063        1,       2
%e A126063        3,       6,       4
%e A126063       15,      30,      20,       8
%e A126063      105,     210,     140,      56,     16
%e A126063      945,    1890,    1260,     504,    144,    32
%e A126063    10395,   20790,   13860,    5544,   1584,   352,    64
%e A126063   135135,  270270,  180180,   72072,  20592,  4576,   832,  128
%p A126063 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 A126063 Flatten[Table[2^k (2n - 1)!!/(2k - 1)!!, {n, 0, 8}, {k, 0, n}]] (* _Ivan Neretin_, May 11 2015 *)
%Y A126063 First column is A001147, second column is A097801.
%Y A126063 The diagonal is A000079, the subdiagonal is A014480.
%K A126063 nonn,tabl,easy
%O A126063 0,3
%A A126063 _N. J. A. Sloane_, Feb 28 2007