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A114192
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Riordan array (1/(1-2x),x/(1-2x)^2).
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2
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1, 2, 1, 4, 6, 1, 8, 24, 10, 1, 16, 80, 60, 14, 1, 32, 240, 280, 112, 18, 1, 64, 672, 1120, 672, 180, 22, 1, 128, 1792, 4032, 3360, 1320, 264, 26, 1, 256, 4608, 13440, 14784, 7920, 2288, 364, 30, 1, 512, 11520, 42240, 59136, 41184, 16016, 3640, 480, 34, 1
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OFFSET
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0,2
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COMMENTS
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Factors as (1/(1-x),x/(1-x))*(1/(1-x),x*(1+x)/(1-x)^2) or A007318 times A114188. Also (1/(1-2*x),x/(1-2*x))*(1,x*(1+2*x)). Inverse is A114193. Row sums are A007583. Diagonal sums are A007051.
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LINKS
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FORMULA
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T(n,k) = sum{j=0..n, C(k, j)*C(n, k+j)}*2^(n-k).
T(n,k) = 4*T(n-1,k) + T(n-1,k-1) - 4*T(n-2,k), T(0,0) = T(1,1) = 1, T(1,0) = 2, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Jan 17 2014
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EXAMPLE
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Triangle begins
1;
2, 1;
4, 6, 1;
8, 24, 10, 1;
16, 80, 60, 14, 1;
32, 240, 280, 112, 18, 1;
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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