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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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13
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| 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 DELEHAM (kolotoko(AT)wanadoo.fr), Oct 20 2007
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FORMULA
| 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.
G.f.: (1-y*x)/(1-2*y*x). DELEHAM Philippe, Feb 04 2012
Sum_{k, 0<=k<=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 . - DELEHAM Philippe, Feb 04 2012
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EXAMPLE
| First few rows of the triangle are:
1;
0, 1;
0, 0, 2;
0, 0, 0, 4;
0, 0, 0, 0, 8;
...
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CROSSREFS
| Cf. A082137, A055372, A057711.
Sequence in context: A171871 A076260 A135416 * A051516 A127391 A204531
Adjacent sequences: A134306 A134307 A134308 * A134310 A134311 A134312
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KEYWORD
| nonn,tabl,changed
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 19 2007
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