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A134309
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Triangle read by rows, where row n consists of n zeros followed by 2^(n-1).
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14
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1, 0, 1, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1024, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2048, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,6
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COMMENTS
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As infinite lower triangular matrices, binomial transform of A134309 = A082137. A134309 * A007318 = A055372. A134309 * [1,2,3,...] = A057711: (1, 2, 6, 16, 40, 96, 224,...).
Triangle read by rows given by [0,0,0,0,0,0,0,0,...] DELTA [1,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Oct 20 2007
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LINKS
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FORMULA
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Triangle, T(0,0) = 1, then for n > 0, n zeros followed by 2^(n-1). Infinite lower triangular matrix with (1, 1, 2, 4, 8, 16, ...) in the main diagonal and the rest zeros.
Sum_{k=0..n} T(n,k)*x^k = A000007(n), A011782(n), A081294(n), A081341(n), A092811(n), A093143(n), A067419(n) for x = 0, 1, 2, 3, 4, 5, 6 respectively. - Philippe Deléham, Feb 04 2012
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EXAMPLE
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Triangle T(n,k) (with rows n >= 0 and columns k = 0..n) begins:
1;
0, 1;
0, 0, 2;
0, 0, 0, 4;
0, 0, 0, 0, 8;
0, 0, 0, 0, 0, 16;
...
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MATHEMATICA
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Join[{1}, Flatten[Table[Join[{PadRight[{}, n], 2^(n-1)}], {n, 20}]]] (* Harvey P. Dale, Jan 04 2024 *)
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PROG
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CROSSREFS
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Cf. A011782 (diagonal elements: 1 followed by 1, 2, 4, 8, ... = A000079: 2^n).
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KEYWORD
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AUTHOR
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STATUS
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approved
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