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A132751
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Triangle T(n, k) = 2/Beta(n-k+1, k) - 1, read by rows.
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2
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1, 3, 3, 5, 11, 5, 7, 23, 23, 7, 9, 39, 59, 39, 9, 11, 59, 119, 119, 59, 11, 13, 83, 209, 279, 209, 83, 13, 15, 111, 335, 559, 559, 335, 111, 15, 17, 143, 503, 1007, 1259, 1007, 503, 143, 17, 19, 179, 719, 1679, 2519, 2519, 1679, 719, 179, 19
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OFFSET
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1,2
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LINKS
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FORMULA
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T(n, k) = 2*A003506(n, k) - 1, an infinite lower triangular matrix.
T(n, k) = 2/Beta(n-k+1, k) - 1.
Sum_{k=1..n} T(n, k) = n*(2^n -1) = A066524(n). (End)
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EXAMPLE
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First few rows of the triangle are:
1;
3, 3;
5, 11, 5;
7, 23, 23, 7;
9, 39, 59, 39, 9;
11, 59, 119, 119, 59, 11;
13, 83, 209, 279, 209, 83, 13;
15, 111, 335, 559, 559, 335, 111, 15;
...
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MATHEMATICA
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T[n_, k_]:= 2/Beta[n-k+1, k] - 1;
Table[T[n, k], {n, 12}, {k, n}]//Flatten (* G. C. Greubel, Feb 16 2021 *)
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PROG
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(Sage)
def A132751(n, k): return 2/beta(n-k+1, k) - 1
(Magma)
A132751:= func< n, k | 2*Factorial(n)/(Factorial(k-1)*Factorial(n-k)) -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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