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A134058
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Triangle T(n, k) = 2*binomial(n, k) with T(0, 0) = 1, read by rows.
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10
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1, 2, 2, 2, 4, 2, 2, 6, 6, 2, 2, 8, 12, 8, 2, 2, 10, 20, 20, 10, 2, 2, 12, 30, 40, 30, 12, 2, 2, 14, 42, 70, 70, 42, 14, 2, 2, 16, 56, 112, 140, 112, 56, 16, 2, 2, 18, 72, 168, 252, 252, 168, 72, 18, 2
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OFFSET
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0,2
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COMMENTS
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Triangle T(n,k), 0 <= k <= n, read by rows, given by [2, -1, 0, 0, 0, 0, 0, ...] DELTA [2, -1, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. - Philippe Deléham, Oct 07 2007
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LINKS
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FORMULA
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Double Pascal's triangle and replace leftmost column with (1,2,2,2,...).
M*A007318, where M = an infinite lower triangular matrix with (1,2,2,2,...) in the main diagonal and the rest zeros.
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EXAMPLE
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First few rows of the triangle:
1
2, 2;
2, 4, 2;
2, 6, 6, 2;
2, 8, 12, 8, 2;
2, 10, 20, 20, 10, 2;
...
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MATHEMATICA
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T[n_, k_]:= SeriesCoefficient[(1+x+y)/(1-x-y), {x, 0, n-k}, {y, 0, k}];
Table[2*Binomial[n, k] -Boole[n==0], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Apr 26 2021 *)
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PROG
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(Magma)
A134058:= func< n, k | n eq 0 select 1 else 2*Binomial(n, k) >;
(Sage)
def A134058(n, k): return 2*binomial(n, k) - bool(n==0)
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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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