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A093423
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Consider the triangle whose first part is shown as an example in the entry A093422. If the n-th term of the triangle read by rows is a fraction then a(n) is the denominator of the fraction, otherwise a(n)=1.
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3
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1, 1, 3, 1, 5, 1, 1, 7, 3, 5, 1, 9, 1, 7, 1, 1, 11, 1, 1, 1, 7, 1, 13, 3, 11, 5, 3, 1, 1, 15, 1, 13, 1, 11, 1, 1, 1, 17, 1, 5, 1, 13, 1, 11, 1, 1, 19, 3, 17, 1, 1, 7, 13, 1, 11, 1, 21, 1, 19, 1, 17, 1, 1, 1, 13, 1, 1, 23, 1, 7, 5, 19, 1, 17, 1, 1, 1, 13
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
1;
1, 3;
1, 5, 1;
1, 7, 3, 5;
1, 9, 1, 7, 1;
1, 11, 1, 1, 1, 7;
1, 13, 3, 11, 5, 3, 1;
1, 15, 1, 13, 1, 11, 1, 1;
...
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MAPLE
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A09342x := proc(n, m) local a, i, N, D ; N := n ; if m = 1 then D := 1 ; else D := n ; end ; for i from 1 to m-1 do N := N*(n-i) ; D := D+n-i ; od ; simplify(N/D) ; end: A093423 := proc(n, m) denom(A09342x(n, m)) ; end: for n from 1 to 12 do for m from 1 to n do printf("%d, ", A093423(n, m)) ; od ; od ; # R. J. Mathar, Apr 28 2007
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MATHEMATICA
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Table[Denominator[2*Binomial[n, k]*(k-1)!/(2*n-k+1)], {n, 1, 30}, {k, 1, n}]//Flatten (* G. C. Greubel, Sep 01 2018 *)
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PROG
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(PARI) for(n=1, 10, for(k=1, n, print1(denominator(2*binomial(n, k)*(k-1)!/(2*n-k+1)), ", "))) \\ G. C. Greubel, Sep 01 2018
(Magma) /* as a triangle */ [[Denominator(2*Binomial(n, k)*Factorial(k-1)/(2*n-k+1)): k in [1..n]]: n in [1..30]]; // G. C. Greubel, Sep 01 2018
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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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