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%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
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