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A188481
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Riordan matrix (1/(1-4x),(1-sqrt(1-4x))/(2*sqrt(1-4x))).
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2
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1, 4, 1, 16, 7, 1, 64, 38, 10, 1, 256, 187, 69, 13, 1, 1024, 874, 406, 109, 16, 1, 4096, 3958, 2186, 748, 158, 19, 1, 16384, 17548, 11124, 4570, 1240, 216, 22, 1, 65536, 76627, 54445, 25879, 8485, 1909, 283, 25, 1, 262144, 330818, 259006, 138917, 52984, 14471, 2782, 359, 28, 1
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OFFSET
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0,2
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COMMENTS
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Inverse matrix: (1/(1+2x)^2, x(1+x)/(1+2x)^2).
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LINKS
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FORMULA
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T(n,k) = [x^n] ((1-sqrt(1-4*x))/(2*sqrt(1-4*x))^k/(1-4*x).
Recurrence: T(n+1,k+1) = T(n,k) + 3*T(n,k-1) + T(n,k-2) - T(n,k-3) + T(n,k-4) - T(n,k-5) + ...
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EXAMPLE
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Triangle begins:
1;
4, 1;
16, 7, 1;
64, 38, 10, 1;
256, 187, 69, 13, 1;
1024, 874, 406, 109, 16, 1;
4096, 3958, 2186, 748, 158, 19, 1;
16384, 17548, 11124, 4570, 1240, 216, 22, 1;
65536, 76627, 54445, 25879, 8485, 1909, 283, 25, 1;
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MATHEMATICA
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Flatten[Table[Sum[Binomial[n+i, n]Binomial[n-i, k]2^(n-k-i), {i, 0, n-k}], {n, 0, 8}, {k, 0, 8}]]
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PROG
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(Maxima) create_list(sum(binomial(n+i, n)*binomial(n-i, k)*2^(n-k-i), i, 0, n-k), n, 0, 8, k, 0, n);
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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