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A114164
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Riordan array (1/(1-2x), x(1-x)/(1-2x)^2).
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3
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1, 2, 1, 4, 5, 1, 8, 18, 8, 1, 16, 56, 41, 11, 1, 32, 160, 170, 73, 14, 1, 64, 432, 620, 377, 114, 17, 1, 128, 1120, 2072, 1666, 704, 164, 20, 1, 256, 2816, 6496, 6608, 3649, 1178, 223, 23, 1, 512, 6912, 19392, 24192, 16722, 7001, 1826, 291, 26, 1, 1024, 16640
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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Number triangle T(n,k) = Sum_{j=0..n} C(n, j)*C(j+k, 2k);
T(n,k) = Sum_{j=0..n} C(n, k+j)*C(k, k-j)*2^(n-k-j)};
T(n, k) = Sum_{j=0..n-k} C(n+k-j, n-k-j)*C(k, j)*(-1)^j*2^(n-k-j).
T(n,k) = 4*T(n-1,k) + T(n-1,k-1) - 4*T(n-2,k) - T(n-2,k-1), 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, 5, 1;
8, 18, 8, 1;
16, 56, 41, 11, 1;
32, 160, 170, 73, 14, 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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